more updates
This commit is contained in:
Morten Hjorth-Jensen
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -424,7 +439,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs008.html">9</a></li>
|
||||
<li><a href="._week42-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -433,7 +448,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs009.html">10</a></li>
|
||||
<li><a href="._week42-bs010.html">11</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs002.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -405,7 +420,7 @@ we will also study the usage of <a href="https://www.youtube.com/watch?v=fRf4l5q
|
||||
<li><a href="._week42-bs010.html">11</a></li>
|
||||
<li><a href="._week42-bs011.html">12</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs003.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -422,7 +437,7 @@ and output layer to any given precision.
|
||||
<li><a href="._week42-bs011.html">12</a></li>
|
||||
<li><a href="._week42-bs012.html">13</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -425,7 +440,7 @@ for the solution to be unique.
|
||||
<li><a href="._week42-bs012.html">13</a></li>
|
||||
<li><a href="._week42-bs013.html">14</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -430,7 +445,7 @@ As described previously, an optimization method could be used to minimize the pa
|
||||
<li><a href="._week42-bs013.html">14</a></li>
|
||||
<li><a href="._week42-bs014.html">15</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -432,7 +447,7 @@ The neural net should then find the parameters \( P \) that minimizes the cost f
|
||||
<li><a href="._week42-bs014.html">15</a></li>
|
||||
<li><a href="._week42-bs015.html">16</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -414,7 +429,7 @@ Automatic differentiation is a method of finding the derivatives numerically wit
|
||||
<li><a href="._week42-bs015.html">16</a></li>
|
||||
<li><a href="._week42-bs016.html">17</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -432,7 +447,7 @@ Having an analytical solution at hand, it is possible to use it to compare how w
|
||||
<li><a href="._week42-bs016.html">17</a></li>
|
||||
<li><a href="._week42-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -423,7 +438,7 @@ In this example, \( \gamma = 2 \) and \( g_0 = 10 \).
|
||||
<li><a href="._week42-bs017.html">18</a></li>
|
||||
<li><a href="._week42-bs018.html">19</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -417,7 +432,7 @@ with \( h_1(x) \) ensuring that \( g_t(x) \) satisfies some conditions and \( h_
|
||||
<li><a href="._week42-bs018.html">19</a></li>
|
||||
<li><a href="._week42-bs019.html">20</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs011.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -429,7 +444,7 @@ $$
|
||||
<li><a href="._week42-bs019.html">20</a></li>
|
||||
<li><a href="._week42-bs020.html">21</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs012.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -438,7 +453,7 @@ is fulfilled as <em>best as possible</em>.
|
||||
<li><a href="._week42-bs020.html">21</a></li>
|
||||
<li><a href="._week42-bs021.html">22</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs013.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -434,7 +449,7 @@ for an input value \( x \).
|
||||
<li><a href="._week42-bs021.html">22</a></li>
|
||||
<li><a href="._week42-bs022.html">23</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs014.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -432,7 +447,7 @@ $$
|
||||
<li><a href="._week42-bs022.html">23</a></li>
|
||||
<li><a href="._week42-bs023.html">24</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs015.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -417,7 +432,7 @@ The input layer will consist of \( N_{\text{input} } \) neurons, passing its ele
|
||||
<li><a href="._week42-bs023.html">24</a></li>
|
||||
<li><a href="._week42-bs024.html">25</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs016.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -426,7 +441,7 @@ $$
|
||||
<li><a href="._week42-bs024.html">25</a></li>
|
||||
<li><a href="._week42-bs025.html">26</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +442,7 @@ $$
|
||||
<li><a href="._week42-bs025.html">26</a></li>
|
||||
<li><a href="._week42-bs026.html">27</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs018.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -442,7 +457,7 @@ it is assumes that the number of neurons in the output layer is one.
|
||||
<li><a href="._week42-bs026.html">27</a></li>
|
||||
<li><a href="._week42-bs027.html">28</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs019.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -425,7 +440,7 @@ $$
|
||||
<li><a href="._week42-bs027.html">28</a></li>
|
||||
<li><a href="._week42-bs028.html">29</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -426,7 +441,7 @@ In this case we seek a continuous range of values since we are approximating a f
|
||||
<li><a href="._week42-bs028.html">29</a></li>
|
||||
<li><a href="._week42-bs029.html">30</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -425,7 +440,7 @@ Here, gradient descent with a constant step size has been chosen.
|
||||
<li><a href="._week42-bs029.html">30</a></li>
|
||||
<li><a href="._week42-bs030.html">31</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -447,7 +462,7 @@ $$
|
||||
<li><a href="._week42-bs030.html">31</a></li>
|
||||
<li><a href="._week42-bs031.html">32</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs023.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -557,7 +572,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs031.html">32</a></li>
|
||||
<li><a href="._week42-bs032.html">33</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -577,7 +592,7 @@ The number of neurons within each hidden layer are given as a list of integers i
|
||||
<li><a href="._week42-bs032.html">33</a></li>
|
||||
<li><a href="._week42-bs033.html">34</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs025.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -429,7 +444,7 @@ Here, we stay with a more simple approach and implement for comparison, the simp
|
||||
<li><a href="._week42-bs033.html">34</a></li>
|
||||
<li><a href="._week42-bs034.html">35</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -425,7 +440,7 @@ In this example, we let \( \alpha = 2 \), \( A = 1 \), and \( g_0 = 1.2 \).
|
||||
<li><a href="._week42-bs034.html">35</a></li>
|
||||
<li><a href="._week42-bs035.html">36</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -430,7 +445,7 @@ $$
|
||||
<li><a href="._week42-bs035.html">36</a></li>
|
||||
<li><a href="._week42-bs036.html">37</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs028.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -579,7 +594,7 @@ The network will be the similar as for the exponential decay example, but with s
|
||||
<li><a href="._week42-bs036.html">37</a></li>
|
||||
<li><a href="._week42-bs037.html">38</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs029.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -533,7 +548,7 @@ extending the program that uses the network using Autograd:
|
||||
<li><a href="._week42-bs037.html">38</a></li>
|
||||
<li><a href="._week42-bs038.html">39</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs030.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -435,7 +450,7 @@ In addition, it could be interesting to see how a typical method for numerically
|
||||
<li><a href="._week42-bs038.html">39</a></li>
|
||||
<li><a href="._week42-bs039.html">40</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs031.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -442,7 +457,7 @@ $$
|
||||
<li><a href="._week42-bs039.html">40</a></li>
|
||||
<li><a href="._week42-bs040.html">41</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs032.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -563,7 +578,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs040.html">41</a></li>
|
||||
<li><a href="._week42-bs041.html">42</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs033.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -502,7 +517,7 @@ which makes it possible to solve for the vector \( \boldsymbol{g} \).
|
||||
<li><a href="._week42-bs041.html">42</a></li>
|
||||
<li><a href="._week42-bs042.html">43</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs034.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -606,7 +621,7 @@ We can then compare the result from this numerical scheme with the output from o
|
||||
<li><a href="._week42-bs042.html">43</a></li>
|
||||
<li><a href="._week42-bs043.html">44</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs035.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +442,7 @@ where \( f \) is an expression involving all kinds of possible mixed derivatives
|
||||
<li><a href="._week42-bs043.html">44</a></li>
|
||||
<li><a href="._week42-bs044.html">45</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs036.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +442,7 @@ The role of the function \( h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P)) \), is to ensu
|
||||
<li><a href="._week42-bs044.html">45</a></li>
|
||||
<li><a href="._week42-bs045.html">46</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +442,7 @@ $$
|
||||
<li><a href="._week42-bs045.html">46</a></li>
|
||||
<li><a href="._week42-bs046.html">47</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs038.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -423,7 +438,7 @@ $$
|
||||
<li><a href="._week42-bs046.html">47</a></li>
|
||||
<li><a href="._week42-bs047.html">48</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs039.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -429,7 +444,7 @@ with \( u(x) \) being some given function.
|
||||
<li><a href="._week42-bs047.html">48</a></li>
|
||||
<li><a href="._week42-bs048.html">49</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs040.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -436,7 +451,7 @@ First, we will look into how Autograd could be used in a network tailored to sol
|
||||
<li><a href="._week42-bs048.html">49</a></li>
|
||||
<li><a href="._week42-bs049.html">50</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs041.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -466,7 +481,7 @@ network at each possible pair \( (x,t) \), given an array for the desired
|
||||
<li><a href="._week42-bs049.html">50</a></li>
|
||||
<li><a href="._week42-bs050.html">51</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs042.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -433,7 +448,7 @@ since \( (0) = u(1) = 0 \) and \( u(x) = \sin(\pi x) \).
|
||||
<li><a href="._week42-bs050.html">51</a></li>
|
||||
<li><a href="._week42-bs051.html">52</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs043.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -471,7 +486,7 @@ mixed derivatives of \( g(x,t) \).
|
||||
<li><a href="._week42-bs051.html">52</a></li>
|
||||
<li><a href="._week42-bs052.html">53</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs044.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -655,7 +670,7 @@ Using TensorFlow results in a much better execution time. Try it!
|
||||
<li><a href="._week42-bs052.html">53</a></li>
|
||||
<li><a href="._week42-bs053.html">54</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs045.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -433,7 +448,7 @@ where \( \frac{\partial g(x,t)}{\partial t} \Big |_{t = 0} \) means the derivati
|
||||
<li><a href="._week42-bs053.html">54</a></li>
|
||||
<li><a href="._week42-bs054.html">55</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs046.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -434,7 +449,7 @@ In this example, let \( c = 1 \) and \( u(x) = \sin(\pi x) \) and \( v(x) = -\pi
|
||||
<li><a href="._week42-bs054.html">55</a></li>
|
||||
<li><a href="._week42-bs055.html">56</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs047.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -428,7 +443,7 @@ Note that this trial solution satisfies the conditions only if \( u(0) = v(0) =
|
||||
<li><a href="._week42-bs055.html">56</a></li>
|
||||
<li><a href="._week42-bs056.html">57</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs048.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -416,7 +431,7 @@ $$
|
||||
<li><a href="._week42-bs056.html">57</a></li>
|
||||
<li><a href="._week42-bs057.html">58</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs049.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -633,7 +648,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs057.html">58</a></li>
|
||||
<li><a href="._week42-bs058.html">59</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs050.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -415,7 +430,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs058.html">59</a></li>
|
||||
<li><a href="._week42-bs059.html">60</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs051.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -443,7 +458,7 @@ Another good read is the article here <a href="https://arxiv.org/pdf/1603.07285.
|
||||
<li><a href="._week42-bs059.html">60</a></li>
|
||||
<li><a href="._week42-bs060.html">61</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs052.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -418,7 +433,7 @@ before the transformation.
|
||||
<li><a href="._week42-bs060.html">61</a></li>
|
||||
<li><a href="._week42-bs061.html">62</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs053.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -432,7 +447,7 @@ in the input).
|
||||
<li><a href="._week42-bs061.html">62</a></li>
|
||||
<li><a href="._week42-bs062.html">63</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs054.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -432,7 +447,7 @@ would quickly lead to possible overfitting.
|
||||
<li><a href="._week42-bs062.html">63</a></li>
|
||||
<li><a href="._week42-bs063.html">64</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs055.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -444,7 +459,7 @@ dimension.
|
||||
<li><a href="._week42-bs063.html">64</a></li>
|
||||
<li><a href="._week42-bs064.html">65</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs056.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -427,7 +442,7 @@ A simple CNN for image classification could have the architecture:
|
||||
<li><a href="._week42-bs064.html">65</a></li>
|
||||
<li><a href="._week42-bs065.html">66</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs057.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -423,7 +438,7 @@ are consistent with the labels in the training set for each image.
|
||||
<li><a href="._week42-bs065.html">66</a></li>
|
||||
<li><a href="._week42-bs066.html">67</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs058.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -425,7 +440,7 @@ and the slides of <a href="http://cs231n.github.io/convolutional-networks/" targ
|
||||
<li><a href="._week42-bs066.html">67</a></li>
|
||||
<li><a href="._week42-bs067.html">68</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs059.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -443,7 +458,7 @@ How can we use this? And what does it mean? Let us study some familiar examples
|
||||
<li><a href="._week42-bs067.html">68</a></li>
|
||||
<li><a href="._week42-bs068.html">69</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs060.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -384,8 +399,24 @@ MathJax.Hub.Config({
|
||||
<h2 id="convolution-examples-polynomial-multiplication" class="anchor">Convolution Examples: Polynomial multiplication </h2>
|
||||
|
||||
<p>
|
||||
We have already met such an example in project 1 when we tried to set up the design matrix for a two-dimensional function.
|
||||
Let us remind of this and recast it in terms of the mathematical operation of convolution.
|
||||
We have already met such an example in project 1 when we tried to set
|
||||
up the design matrix for a two-dimensional function. This was an
|
||||
example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.
|
||||
Let us look a the following polynomials to second and third order, respectively:
|
||||
$$
|
||||
p(t) = \alpha_0+\alpha_1 t+\alpha_2 t^2,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
s(t) = \beta_0+\beta_1 t+\beta_2 t^2+\beta_3 t^3.
|
||||
$$
|
||||
|
||||
<p>
|
||||
The polynomial multiplication gives us a new polynomial of degree \( 5 \)
|
||||
$$
|
||||
z(t) = \delta_0+\delta_1 t+\delta_2 t^2+\delta_3 t^3+\delta_4 t^4+\delta_5 t^5.
|
||||
$$
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -413,7 +444,7 @@ Let us remind of this and recast it in terms of the mathematical operation of co
|
||||
<li><a href="._week42-bs068.html">69</a></li>
|
||||
<li><a href="._week42-bs069.html">70</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs061.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,7 +396,39 @@ MathJax.Hub.Config({
|
||||
<a name="part0061"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="convolution-examples-probability-theory" class="anchor">Convolution Examples: Probability Theory </h2>
|
||||
<h2 id="efficient-polynomial-multiplication" class="anchor">Efficient Polynomial Multiplication </h2>
|
||||
|
||||
<p>
|
||||
Computing polynomial products can be implemented efficiently if we rewrite the the more brute force multiplications using convolution.
|
||||
We note first that the new coefficients are given as
|
||||
|
||||
$$
|
||||
\begin{split}
|
||||
\delta_0=&\alpha_0\beta_0\\
|
||||
\delta_1=&\alpha_1\beta_0+\beta_0\alpha_1\\
|
||||
\delta_2=&\alpha_0\beta_2+\beta_1\alpha_1+\alpha_2\beta_0\\
|
||||
\delta_3=&\alpha_1\beta_2+\beta_1\alpha_2+\alpha_0\beta_3\\
|
||||
\delta_4=&\alpha_2\beta_2+\beta_3\alpha_1\\
|
||||
\delta_5=&\alpha_2\beta_3.\\
|
||||
\end{split}
|
||||
$$
|
||||
|
||||
<p>
|
||||
We note that \( \alpha_i=0 \) except for \( i\in \left{0,1,2\right} \) and \( \beta_i=0 \) except for \( i\in\left{0,1,2,3\right} \).
|
||||
|
||||
<p>
|
||||
We can then rewrite the coefficients \( \delta_j \) using a discrete convolution as
|
||||
$$
|
||||
\delta_j = \sum_{i=-\infty}^{i=\infty}\alpha_i\beta_{j-i}=(\alpha * \beta)_j,
|
||||
$$
|
||||
|
||||
or as a double sum with restriction \( l=i+j \)
|
||||
$$
|
||||
\delta_l = \sum_{ij}\alpha_i\beta_{j}.
|
||||
$$
|
||||
|
||||
<p>
|
||||
Do you see a potential drawback with these equations?
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -409,7 +456,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs069.html">70</a></li>
|
||||
<li><a href="._week42-bs070.html">71</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs062.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,27 +396,25 @@ MathJax.Hub.Config({
|
||||
<a name="part0062"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" class="anchor">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms) </h2>
|
||||
<h2 id="a-more-efficient-way-of-coding-the-above-convolution" class="anchor">A more efficient way of coding the above Convolution </h2>
|
||||
|
||||
<p>
|
||||
For problems with so-called harmonic oscillations, given by for example the following differential equation
|
||||
$$
|
||||
m\frac{d^2x(t)}(dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
$$
|
||||
Since we only have a finite number of \( \alpha \) and \( \beta \) values
|
||||
which are non-zero, we can rewrite the above convolution expressions
|
||||
as a matrix-vector multiplication
|
||||
|
||||
where \( F(t) \) is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.
|
||||
$$
|
||||
\boldsymbol{\delta}=\begin{bmatriax}\alpha_0 & 0 & 0 & 0 \\
|
||||
\alpha_1 & \alpha_0 & 0 & 0 \\
|
||||
\alpha_2 & \alpha_1 & \alpha_0 & 0 \\
|
||||
0 & \alpha_2 & \alpha_1 & \alpha_0 \\
|
||||
0 & 0 & \alpha_2 & \alpha_1 \\
|
||||
0 & 0 & 0 & \alpha_2
|
||||
\end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3\end{bmatrix}
|
||||
$$
|
||||
|
||||
<p>
|
||||
If one has several driving forces, \( F(t)=\sum_n F_n(t) \), one can find
|
||||
the particular solution to each \( F_n \), \( x_{pn}(t) \), and the particular
|
||||
solution for the entire driving force is then given by a series like
|
||||
|
||||
$$
|
||||
\begin{equation}
|
||||
x_p(t)=\sum_nx_{pn}(t).
|
||||
\tag{21}
|
||||
\end{equation}
|
||||
$$
|
||||
The process is commutative and we can easily see that we can rewrite the multiplication in terms of a martrix holding \( \beta \) and a vector holding \( \alpha \).
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -429,7 +442,7 @@ $$
|
||||
<li><a href="._week42-bs070.html">71</a></li>
|
||||
<li><a href="._week42-bs071.html">72</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs063.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,32 +396,27 @@ MathJax.Hub.Config({
|
||||
<a name="part0063"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="principle-of-superposition" class="anchor">Principle of Superposition </h2>
|
||||
<h2 id="convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" class="anchor">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms) </h2>
|
||||
|
||||
<p>
|
||||
This is known as the principle of superposition. It only applies when
|
||||
the homogenous equation is linear. If there were an anharmonic term
|
||||
such as \( x^3 \) in the homogenous equation, then when one summed various
|
||||
solutions, \( x=(\sum_n x_n)^2 \), one would get cross
|
||||
terms. Superposition is especially useful when \( F(t) \) can be written
|
||||
as a sum of sinusoidal terms, because the solutions for each
|
||||
sinusoidal (sine or cosine) term is analytic.
|
||||
|
||||
<p>
|
||||
Driving forces are often periodic, even when they are not
|
||||
sinusoidal. Periodicity implies that for some time \( \tau \)
|
||||
|
||||
For problems with so-called harmonic oscillations, given by for example the following differential equation
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
F(t+\tau)=F(t).
|
||||
\end{eqnarray}
|
||||
m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
$$
|
||||
|
||||
where \( F(t) \) is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.
|
||||
|
||||
<p>
|
||||
One example of a non-sinusoidal periodic force is a square wave. Many
|
||||
components in electric circuits are non-linear, e.g. diodes, which
|
||||
makes many wave forms non-sinusoidal even when the circuits are being
|
||||
driven by purely sinusoidal sources.
|
||||
If one has several driving forces, \( F(t)=\sum_n F_n(t) \), one can find
|
||||
the particular solution to each \( F_n \), \( x_{pn}(t) \), and the particular
|
||||
solution for the entire driving force is then given by a series like
|
||||
|
||||
$$
|
||||
\begin{equation}
|
||||
x_p(t)=\sum_nx_{pn}(t).
|
||||
\tag{21}
|
||||
\end{equation}
|
||||
$$
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -434,7 +444,7 @@ driven by purely sinusoidal sources.
|
||||
<li><a href="._week42-bs071.html">72</a></li>
|
||||
<li><a href="._week42-bs072.html">73</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs064.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,46 +396,33 @@ MathJax.Hub.Config({
|
||||
<a name="part0064"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="simple-code-example" class="anchor">Simple Code Example </h2>
|
||||
<h2 id="principle-of-superposition" class="anchor">Principle of Superposition </h2>
|
||||
|
||||
<p>
|
||||
The code here shows a typical example of such a square wave generated using the functionality included in the <b>scipy</b> Python package. We have used a period of \( \tau=0.2 \).
|
||||
This is known as the principle of superposition. It only applies when
|
||||
the homogenous equation is linear. If there were an anharmonic term
|
||||
such as \( x^3 \) in the homogenous equation, then when one summed various
|
||||
solutions, \( x=(\sum_n x_n)^2 \), one would get cross
|
||||
terms. Superposition is especially useful when \( F(t) \) can be written
|
||||
as a sum of sinusoidal terms, because the solutions for each
|
||||
sinusoidal (sine or cosine) term is analytic.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">math</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">scipy</span> <span style="color: #008000; font-weight: bold">import</span> signal
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
|
||||
<span style="color: #408080; font-style: italic"># number of points </span>
|
||||
n <span style="color: #666666">=</span> <span style="color: #666666">500</span>
|
||||
<span style="color: #408080; font-style: italic"># start and final times </span>
|
||||
t0 <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
|
||||
tn <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
|
||||
<span style="color: #408080; font-style: italic"># Period </span>
|
||||
t <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(t0, tn, n, endpoint<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)
|
||||
SqrSignal <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(n)
|
||||
SqrSignal <span style="color: #666666">=</span> <span style="color: #666666">1.0+</span>signal<span style="color: #666666">.</span>square(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*5*</span>t)
|
||||
plt<span style="color: #666666">.</span>plot(t, SqrSignal)
|
||||
plt<span style="color: #666666">.</span>ylim(<span style="color: #666666">-0.5</span>, <span style="color: #666666">2.5</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
For the sinusoidal example the
|
||||
period is \( \tau=2\pi/\omega \). However, higher harmonics can also
|
||||
satisfy the periodicity requirement. In general, any force that
|
||||
satisfies the periodicity requirement can be expressed as a sum over
|
||||
harmonics,
|
||||
Driving forces are often periodic, even when they are not
|
||||
sinusoidal. Periodicity implies that for some time \( \tau \)
|
||||
|
||||
$$
|
||||
\begin{equation}
|
||||
F(t)=\frac{f_0}{2}+\sum_{n>0} f_n\cos(2n\pi t/\tau)+g_n\sin(2n\pi t/\tau).
|
||||
\tag{22}
|
||||
\end{equation}
|
||||
\begin{eqnarray}
|
||||
F(t+\tau)=F(t).
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
One example of a non-sinusoidal periodic force is a square wave. Many
|
||||
components in electric circuits are non-linear, e.g. diodes, which
|
||||
makes many wave forms non-sinusoidal even when the circuits are being
|
||||
driven by purely sinusoidal sources.
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -447,7 +449,7 @@ $$
|
||||
<li><a href="._week42-bs072.html">73</a></li>
|
||||
<li><a href="._week42-bs073.html">74</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs065.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,37 +396,46 @@ MathJax.Hub.Config({
|
||||
<a name="part0065"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="wrapping-up-fourier-transforms" class="anchor">Wrapping up Fourier transforms </h2>
|
||||
<h2 id="simple-code-example" class="anchor">Simple Code Example </h2>
|
||||
|
||||
<p>
|
||||
We can write down the answer for
|
||||
\( x_{pn}(t) \), by substituting \( f_n/m \) or \( g_n/m \) for \( F_0/m \). By
|
||||
writing each factor \( 2n\pi t/\tau \) as \( n\omega t \), with \( \omega\equiv
|
||||
2\pi/\tau \),
|
||||
The code here shows a typical example of such a square wave generated using the functionality included in the <b>scipy</b> Python package. We have used a period of \( \tau=0.2 \).
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">math</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">scipy</span> <span style="color: #008000; font-weight: bold">import</span> signal
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
|
||||
<span style="color: #408080; font-style: italic"># number of points </span>
|
||||
n <span style="color: #666666">=</span> <span style="color: #666666">500</span>
|
||||
<span style="color: #408080; font-style: italic"># start and final times </span>
|
||||
t0 <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
|
||||
tn <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
|
||||
<span style="color: #408080; font-style: italic"># Period </span>
|
||||
t <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(t0, tn, n, endpoint<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)
|
||||
SqrSignal <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(n)
|
||||
SqrSignal <span style="color: #666666">=</span> <span style="color: #666666">1.0+</span>signal<span style="color: #666666">.</span>square(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*5*</span>t)
|
||||
plt<span style="color: #666666">.</span>plot(t, SqrSignal)
|
||||
plt<span style="color: #666666">.</span>ylim(<span style="color: #666666">-0.5</span>, <span style="color: #666666">2.5</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
For the sinusoidal example the
|
||||
period is \( \tau=2\pi/\omega \). However, higher harmonics can also
|
||||
satisfy the periodicity requirement. In general, any force that
|
||||
satisfies the periodicity requirement can be expressed as a sum over
|
||||
harmonics,
|
||||
|
||||
$$
|
||||
\begin{equation}
|
||||
\tag{23}
|
||||
F(t)=\frac{f_0}{2}+\sum_{n>0}f_n\cos(n\omega t)+g_n\sin(n\omega t).
|
||||
F(t)=\frac{f_0}{2}+\sum_{n>0} f_n\cos(2n\pi t/\tau)+g_n\sin(2n\pi t/\tau).
|
||||
\tag{22}
|
||||
\end{equation}
|
||||
$$
|
||||
|
||||
<p>
|
||||
The solutions for \( x(t) \) then come from replacing \( \omega \) with
|
||||
\( n\omega \) for each term in the particular solution,
|
||||
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
x_p(t)&=&\frac{f_0}{2k}+\sum_{n>0} \alpha_n\cos(n\omega t-\delta_n)+\beta_n\sin(n\omega t-\delta_n),\\
|
||||
\nonumber
|
||||
\alpha_n&=&\frac{f_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\
|
||||
\nonumber
|
||||
\beta_n&=&\frac{g_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\
|
||||
\nonumber
|
||||
\delta_n&=&\tan^{-1}\left(\frac{2\beta n\omega}{\omega_0^2-n^2\omega^2}\right).
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -438,7 +462,7 @@ $$
|
||||
<li><a href="._week42-bs073.html">74</a></li>
|
||||
<li><a href="._week42-bs074.html">75</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs066.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,73 +396,37 @@ MathJax.Hub.Config({
|
||||
<a name="part0066"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="finding-the-coefficients" class="anchor">Finding the Coefficients </h2>
|
||||
<h2 id="wrapping-up-fourier-transforms" class="anchor">Wrapping up Fourier transforms </h2>
|
||||
|
||||
<p>
|
||||
Because the forces have been applied for a long time, any non-zero
|
||||
damping eliminates the homogenous parts of the solution, so one need
|
||||
only consider the particular solution for each \( n \).
|
||||
|
||||
<p>
|
||||
The problem is considered solved if one can find expressions for the
|
||||
coefficients \( f_n \) and \( g_n \), even though the solutions are expressed
|
||||
as an infinite sum. The coefficients can be extracted from the
|
||||
function \( F(t) \) by
|
||||
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
\tag{24}
|
||||
f_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\cos(2n\pi t/\tau),\\
|
||||
\nonumber
|
||||
g_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\sin(2n\pi t/\tau).
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
To check the consistency of these expressions and to verify
|
||||
Eq. <a href="#mjx-eqn-24">(24)</a>, one can insert the expansion of \( F(t) \) in
|
||||
Eq. <a href="._week42-bs065.html#mjx-eqn-23">(23)</a> into the expression for the coefficients in
|
||||
Eq. <a href="#mjx-eqn-24">(24)</a> and see whether
|
||||
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~\left\{
|
||||
\frac{f_0}{2}+\sum_{m>0}f_m\cos(m\omega t)+g_m\sin(m\omega t)
|
||||
\right\}\cos(n\omega t).
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
Immediately, one can throw away all the terms with \( g_m \) because they
|
||||
convolute an even and an odd function. The term with \( f_0/2 \)
|
||||
disappears because \( \cos(n\omega t) \) is equally positive and negative
|
||||
over the interval and will integrate to zero. For all the terms
|
||||
\( f_m\cos(m\omega t) \) appearing in the sum, one can use angle addition
|
||||
formulas to see that \( \cos(m\omega t)\cos(n\omega
|
||||
t)=(1/2)(\cos[(m+n)\omega t]+\cos[(m-n)\omega t] \). This will integrate
|
||||
to zero unless \( m=n \). In that case the \( m=n \) term gives
|
||||
We can write down the answer for
|
||||
\( x_{pn}(t) \), by substituting \( f_n/m \) or \( g_n/m \) for \( F_0/m \). By
|
||||
writing each factor \( 2n\pi t/\tau \) as \( n\omega t \), with \( \omega\equiv
|
||||
2\pi/\tau \),
|
||||
|
||||
$$
|
||||
\begin{equation}
|
||||
\int_{-\tau/2}^{\tau/2}dt~\cos^2(m\omega t)=\frac{\tau}{2},
|
||||
\tag{25}
|
||||
\tag{23}
|
||||
F(t)=\frac{f_0}{2}+\sum_{n>0}f_n\cos(n\omega t)+g_n\sin(n\omega t).
|
||||
\end{equation}
|
||||
$$
|
||||
|
||||
<p>
|
||||
and
|
||||
The solutions for \( x(t) \) then come from replacing \( \omega \) with
|
||||
\( n\omega \) for each term in the particular solution,
|
||||
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~f_n/2\\
|
||||
x_p(t)&=&\frac{f_0}{2k}+\sum_{n>0} \alpha_n\cos(n\omega t-\delta_n)+\beta_n\sin(n\omega t-\delta_n),\\
|
||||
\nonumber
|
||||
&=&f_n~\checkmark.
|
||||
\alpha_n&=&\frac{f_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\
|
||||
\nonumber
|
||||
\beta_n&=&\frac{g_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\
|
||||
\nonumber
|
||||
\delta_n&=&\tan^{-1}\left(\frac{2\beta n\omega}{\omega_0^2-n^2\omega^2}\right).
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
The same method can be used to check for the consistency of \( g_n \).
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -474,7 +453,7 @@ The same method can be used to check for the consistency of \( g_n \).
|
||||
<li><a href="._week42-bs074.html">75</a></li>
|
||||
<li><a href="._week42-bs075.html">76</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs067.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,18 +396,72 @@ MathJax.Hub.Config({
|
||||
<a name="part0067"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" class="anchor">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras </h2>
|
||||
<h2 id="finding-the-coefficients" class="anchor">Finding the Coefficients </h2>
|
||||
|
||||
<p>
|
||||
As discussed above, CNNs are neural networks built from the assumption that the inputs
|
||||
to the network are 2D images. This is important because the number of features or pixels in images
|
||||
grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.
|
||||
Because the forces have been applied for a long time, any non-zero
|
||||
damping eliminates the homogenous parts of the solution, so one need
|
||||
only consider the particular solution for each \( n \).
|
||||
|
||||
<p>
|
||||
As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks
|
||||
are the <b>convolutional</b> and <b>pooling</b> layers stacked in pairs between the input and the hidden layer.
|
||||
In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D
|
||||
matrices, typically 1 for each color dimension (Red, Green, Blue).
|
||||
The problem is considered solved if one can find expressions for the
|
||||
coefficients \( f_n \) and \( g_n \), even though the solutions are expressed
|
||||
as an infinite sum. The coefficients can be extracted from the
|
||||
function \( F(t) \) by
|
||||
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
\tag{24}
|
||||
f_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\cos(2n\pi t/\tau),\\
|
||||
\nonumber
|
||||
g_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\sin(2n\pi t/\tau).
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
To check the consistency of these expressions and to verify
|
||||
Eq. <a href="#mjx-eqn-24">(24)</a>, one can insert the expansion of \( F(t) \) in
|
||||
Eq. <a href="._week42-bs066.html#mjx-eqn-23">(23)</a> into the expression for the coefficients in
|
||||
Eq. <a href="#mjx-eqn-24">(24)</a> and see whether
|
||||
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~\left\{
|
||||
\frac{f_0}{2}+\sum_{m>0}f_m\cos(m\omega t)+g_m\sin(m\omega t)
|
||||
\right\}\cos(n\omega t).
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
Immediately, one can throw away all the terms with \( g_m \) because they
|
||||
convolute an even and an odd function. The term with \( f_0/2 \)
|
||||
disappears because \( \cos(n\omega t) \) is equally positive and negative
|
||||
over the interval and will integrate to zero. For all the terms
|
||||
\( f_m\cos(m\omega t) \) appearing in the sum, one can use angle addition
|
||||
formulas to see that \( \cos(m\omega t)\cos(n\omega
|
||||
t)=(1/2)(\cos[(m+n)\omega t]+\cos[(m-n)\omega t] \). This will integrate
|
||||
to zero unless \( m=n \). In that case the \( m=n \) term gives
|
||||
|
||||
$$
|
||||
\begin{equation}
|
||||
\int_{-\tau/2}^{\tau/2}dt~\cos^2(m\omega t)=\frac{\tau}{2},
|
||||
\tag{25}
|
||||
\end{equation}
|
||||
$$
|
||||
|
||||
<p>
|
||||
and
|
||||
|
||||
$$
|
||||
\begin{eqnarray}
|
||||
f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~f_n/2\\
|
||||
\nonumber
|
||||
&=&f_n~\checkmark.
|
||||
\end{eqnarray}
|
||||
$$
|
||||
|
||||
<p>
|
||||
The same method can be used to check for the consistency of \( g_n \).
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -420,7 +489,7 @@ matrices, typically 1 for each color dimension (Red, Green, Blue).
|
||||
<li><a href="._week42-bs075.html">76</a></li>
|
||||
<li><a href="._week42-bs076.html">77</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs068.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,15 +396,50 @@ MathJax.Hub.Config({
|
||||
<a name="part0068"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="setting-it-up" class="anchor">Setting it up </h2>
|
||||
<h2 id="final-words-on-fourier-transforms" class="anchor">Final words on Fourier Transforms </h2>
|
||||
|
||||
<p>
|
||||
It means that to represent the entire
|
||||
dataset of images, we require a 4D matrix or <b>tensor</b>. This tensor has the dimensions:
|
||||
$$
|
||||
(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
|
||||
$$
|
||||
The code here uses the Fourier series applied to a
|
||||
square wave signal. The code here
|
||||
visualizes the various approximations given by Fourier series compared
|
||||
with a square wave with period \( T=0.2 \) (dimensionless time), width \( 0.1 \) and max value of the force \( F=2 \). We
|
||||
see that when we increase the number of components in the Fourier
|
||||
series, the Fourier series approximation gets closer and closer to the
|
||||
square wave signal.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">math</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">scipy</span> <span style="color: #008000; font-weight: bold">import</span> signal
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
|
||||
<span style="color: #408080; font-style: italic"># number of points </span>
|
||||
n <span style="color: #666666">=</span> <span style="color: #666666">500</span>
|
||||
<span style="color: #408080; font-style: italic"># start and final times </span>
|
||||
t0 <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
|
||||
tn <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
|
||||
<span style="color: #408080; font-style: italic"># Period </span>
|
||||
T <span style="color: #666666">=0.2</span>
|
||||
<span style="color: #408080; font-style: italic"># Max value of square signal </span>
|
||||
Fmax<span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
|
||||
<span style="color: #408080; font-style: italic"># Width of signal </span>
|
||||
Width <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
|
||||
t <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(t0, tn, n, endpoint<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)
|
||||
SqrSignal <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(n)
|
||||
FourierSeriesSignal <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(n)
|
||||
SqrSignal <span style="color: #666666">=</span> <span style="color: #666666">1.0+</span>signal<span style="color: #666666">.</span>square(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*5*</span>t<span style="color: #666666">+</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>Width<span style="color: #666666">/</span>T)
|
||||
a0 <span style="color: #666666">=</span> Fmax<span style="color: #666666">*</span>Width<span style="color: #666666">/</span>T
|
||||
FourierSeriesSignal <span style="color: #666666">=</span> a0
|
||||
Factor <span style="color: #666666">=</span> <span style="color: #666666">2.0*</span>Fmax<span style="color: #666666">/</span>np<span style="color: #666666">.</span>pi
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,<span style="color: #666666">500</span>):
|
||||
FourierSeriesSignal <span style="color: #666666">+=</span> Factor<span style="color: #666666">/</span>(i)<span style="color: #666666">*</span>np<span style="color: #666666">.</span>sin(np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>i<span style="color: #666666">*</span>Width<span style="color: #666666">/</span>T)<span style="color: #666666">*</span>np<span style="color: #666666">.</span>cos(i<span style="color: #666666">*</span>t<span style="color: #666666">*2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">/</span>T)
|
||||
plt<span style="color: #666666">.</span>plot(t, SqrSignal)
|
||||
plt<span style="color: #666666">.</span>plot(t, FourierSeriesSignal)
|
||||
plt<span style="color: #666666">.</span>ylim(<span style="color: #666666">-0.5</span>, <span style="color: #666666">2.5</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -416,7 +466,7 @@ $$
|
||||
<li><a href="._week42-bs076.html">77</a></li>
|
||||
<li><a href="._week42-bs077.html">78</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs069.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,20 +396,10 @@ MathJax.Hub.Config({
|
||||
<a name="part0069"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="the-mnist-dataset-again" class="anchor">The MNIST dataset again </h2>
|
||||
<h2 id="convolution-examples-probability-theory" class="anchor">Convolution Examples: Probability Theory </h2>
|
||||
|
||||
<p>
|
||||
The MNIST dataset consists of grayscale images with a pixel size of
|
||||
\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each
|
||||
neuron in the first hidden layer.
|
||||
|
||||
<p>
|
||||
If we were to analyze images of size \( 128\times 128 \) we would require
|
||||
\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were
|
||||
dealing with color images, as most images are, we have an image matrix
|
||||
of size \( 128\times 128 \) for each color dimension (Red, Green, Blue),
|
||||
meaning 3 times the number of weights \( = 49152 \) are required for every
|
||||
single neuron in the first hidden layer.
|
||||
More text will be added here
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -422,7 +427,7 @@ single neuron in the first hidden layer.
|
||||
<li><a href="._week42-bs077.html">78</a></li>
|
||||
<li><a href="._week42-bs078.html">79</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs070.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,20 +396,18 @@ MathJax.Hub.Config({
|
||||
<a name="part0070"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="strong-correlations" class="anchor">Strong correlations </h2>
|
||||
<h2 id="cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" class="anchor">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
<p>
|
||||
Images typically have strong local correlations, meaning that a small
|
||||
part of the image varies little from its neighboring regions. If for
|
||||
example we have an image of a blue car, we can roughly assume that a
|
||||
small blue part of the image is surrounded by other blue regions.
|
||||
As discussed above, CNNs are neural networks built from the assumption that the inputs
|
||||
to the network are 2D images. This is important because the number of features or pixels in images
|
||||
grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.
|
||||
|
||||
<p>
|
||||
Therefore, instead of connecting every single pixel to a neuron in the
|
||||
first hidden layer, as we have previously done with deep neural
|
||||
networks, we can instead connect each neuron to a small part of the
|
||||
image (in all 3 RGB depth dimensions). The size of each small area is
|
||||
fixed, and known as a <a href="https://en.wikipedia.org/wiki/Receptive_field" target="_self">receptive</a>.
|
||||
As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks
|
||||
are the <b>convolutional</b> and <b>pooling</b> layers stacked in pairs between the input and the hidden layer.
|
||||
In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D
|
||||
matrices, typically 1 for each color dimension (Red, Green, Blue).
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -422,7 +435,7 @@ fixed, and known as a <a href="https://en.wikipedia.org/wiki/Receptive_field" ta
|
||||
<li><a href="._week42-bs078.html">79</a></li>
|
||||
<li><a href="._week42-bs079.html">80</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs071.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -379,26 +394,16 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0071"></a>
|
||||
<!-- !split -->
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="layers-of-a-cnn" class="anchor">Layers of a CNN </h2>
|
||||
The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.
|
||||
The input image is typically a square matrix of depth 3.
|
||||
<h2 id="setting-it-up" class="anchor">Setting it up </h2>
|
||||
|
||||
<p>
|
||||
A <b>convolution</b> is performed on the image which outputs
|
||||
a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as <b>filters</b>.
|
||||
|
||||
<p>
|
||||
Each filter slides along the input image, taking the dot product
|
||||
between each small part of the image and the filter, in all depth
|
||||
dimensions. This is then passed through a non-linear function,
|
||||
typically the <b>Rectified Linear (ReLu)</b> function, which serves as the
|
||||
activation of the neurons in the first convolutional layer. This is
|
||||
further passed through a <b>pooling layer</b>, which reduces the size of the
|
||||
convolutional layer, e.g. by taking the maximum or average across some
|
||||
small regions, and this serves as input to the next convolutional
|
||||
layer.
|
||||
It means that to represent the entire
|
||||
dataset of images, we require a 4D matrix or <b>tensor</b>. This tensor has the dimensions:
|
||||
$$
|
||||
(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
|
||||
$$
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -426,7 +431,7 @@ layer.
|
||||
<li><a href="._week42-bs079.html">80</a></li>
|
||||
<li><a href="._week42-bs080.html">81</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs072.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,17 +396,20 @@ MathJax.Hub.Config({
|
||||
<a name="part0072"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="systematic-reduction" class="anchor">Systematic reduction </h2>
|
||||
<h2 id="the-mnist-dataset-again" class="anchor">The MNIST dataset again </h2>
|
||||
|
||||
<p>
|
||||
By systematically reducing the size of the input volume, through
|
||||
convolution and pooling, the network should create representations of
|
||||
small parts of the input, and then from them assemble representations
|
||||
of larger areas. The final pooling layer is flattened to serve as
|
||||
input to a hidden layer, such that each neuron in the final pooling
|
||||
layer is connected to every single neuron in the hidden layer. This
|
||||
then serves as input to the output layer, e.g. a softmax output for
|
||||
classification.
|
||||
The MNIST dataset consists of grayscale images with a pixel size of
|
||||
\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each
|
||||
neuron in the first hidden layer.
|
||||
|
||||
<p>
|
||||
If we were to analyze images of size \( 128\times 128 \) we would require
|
||||
\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were
|
||||
dealing with color images, as most images are, we have an image matrix
|
||||
of size \( 128\times 128 \) for each color dimension (Red, Green, Blue),
|
||||
meaning 3 times the number of weights \( = 49152 \) are required for every
|
||||
single neuron in the first hidden layer.
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -419,7 +437,7 @@ classification.
|
||||
<li><a href="._week42-bs080.html">81</a></li>
|
||||
<li><a href="._week42-bs081.html">82</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs073.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,51 +396,21 @@ MathJax.Hub.Config({
|
||||
<a name="part0073"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="prerequisites-collect-and-pre-process-data" class="anchor">Prerequisites: Collect and pre-process data </h2>
|
||||
<h2 id="strong-correlations" class="anchor">Strong correlations </h2>
|
||||
|
||||
<p>
|
||||
Images typically have strong local correlations, meaning that a small
|
||||
part of the image varies little from its neighboring regions. If for
|
||||
example we have an image of a blue car, we can roughly assume that a
|
||||
small blue part of the image is surrounded by other blue regions.
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #408080; font-style: italic"># import necessary packages</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
<p>
|
||||
Therefore, instead of connecting every single pixel to a neuron in the
|
||||
first hidden layer, as we have previously done with deep neural
|
||||
networks, we can instead connect each neuron to a small part of the
|
||||
image (in all 3 RGB depth dimensions). The size of each small area is
|
||||
fixed, and known as a <a href="https://en.wikipedia.org/wiki/Receptive_field" target="_self">receptive</a>.
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># ensure the same random numbers appear every time</span>
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># display images in notebook</span>
|
||||
<span style="color: #666666">%</span>matplotlib inline
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'figure.figsize'</span>] <span style="color: #666666">=</span> (<span style="color: #666666">12</span>,<span style="color: #666666">12</span>)
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># download MNIST dataset</span>
|
||||
digits <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_digits()
|
||||
|
||||
<span style="color: #408080; font-style: italic"># define inputs and labels</span>
|
||||
inputs <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>images
|
||||
labels <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>target
|
||||
|
||||
<span style="color: #408080; font-style: italic"># RGB images have a depth of 3</span>
|
||||
<span style="color: #408080; font-style: italic"># our images are grayscale so they should have a depth of 1</span>
|
||||
inputs <span style="color: #666666">=</span> inputs[:,:,:,np<span style="color: #666666">.</span>newaxis]
|
||||
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"inputs = (n_inputs, pixel_width, pixel_height, depth) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
|
||||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"labels = (n_inputs) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(labels<span style="color: #666666">.</span>shape))
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># choose some random images to display</span>
|
||||
n_inputs <span style="color: #666666">=</span> <span style="color: #008000">len</span>(inputs)
|
||||
indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(n_inputs)
|
||||
random_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(indices, size<span style="color: #666666">=5</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, image <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(digits<span style="color: #666666">.</span>images[random_indices]):
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">1</span>, <span style="color: #666666">5</span>, i<span style="color: #666666">+1</span>)
|
||||
plt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">'off'</span>)
|
||||
plt<span style="color: #666666">.</span>imshow(image, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>gray_r, interpolation<span style="color: #666666">=</span><span style="color: #BA2121">'nearest'</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Label: </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> digits<span style="color: #666666">.</span>target[random_indices[i]])
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -452,7 +437,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._week42-bs081.html">82</a></li>
|
||||
<li><a href="._week42-bs082.html">83</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs074.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -379,35 +394,27 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0074"></a>
|
||||
<!-- !split -->
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="layers-of-a-cnn" class="anchor">Layers of a CNN </h2>
|
||||
The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.
|
||||
The input image is typically a square matrix of depth 3.
|
||||
|
||||
<h2 id="importing-keras-and-tensorflow" class="anchor">Importing Keras and Tensorflow </h2>
|
||||
<p>
|
||||
A <b>convolution</b> is performed on the image which outputs
|
||||
a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as <b>filters</b>.
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">tensorflow.keras</span> <span style="color: #008000; font-weight: bold">import</span> datasets, layers, models
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">tensorflow.keras.layers</span> <span style="color: #008000; font-weight: bold">import</span> Input
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">tensorflow.keras.models</span> <span style="color: #008000; font-weight: bold">import</span> Sequential <span style="color: #408080; font-style: italic">#This allows appending layers to existing models</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">tensorflow.keras.layers</span> <span style="color: #008000; font-weight: bold">import</span> Dense <span style="color: #408080; font-style: italic">#This allows defining the characteristics of a particular layer</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">tensorflow.keras</span> <span style="color: #008000; font-weight: bold">import</span> optimizers <span style="color: #408080; font-style: italic">#This allows using whichever optimiser we want (sgd,adam,RMSprop)</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">tensorflow.keras</span> <span style="color: #008000; font-weight: bold">import</span> regularizers <span style="color: #408080; font-style: italic">#This allows using whichever regularizer we want (l1,l2,l1_l2)</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">tensorflow.keras.utils</span> <span style="color: #008000; font-weight: bold">import</span> to_categorical <span style="color: #408080; font-style: italic">#This allows using categorical cross entropy as the cost function</span>
|
||||
<span style="color: #408080; font-style: italic">#from tensorflow.keras import Conv2D</span>
|
||||
<span style="color: #408080; font-style: italic">#from tensorflow.keras import MaxPooling2D</span>
|
||||
<span style="color: #408080; font-style: italic">#from tensorflow.keras import Flatten</span>
|
||||
<p>
|
||||
Each filter slides along the input image, taking the dot product
|
||||
between each small part of the image and the filter, in all depth
|
||||
dimensions. This is then passed through a non-linear function,
|
||||
typically the <b>Rectified Linear (ReLu)</b> function, which serves as the
|
||||
activation of the neurons in the first convolutional layer. This is
|
||||
further passed through a <b>pooling layer</b>, which reduces the size of the
|
||||
convolutional layer, e.g. by taking the maximum or average across some
|
||||
small regions, and this serves as input to the next convolutional
|
||||
layer.
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
|
||||
|
||||
<span style="color: #408080; font-style: italic"># representation of labels</span>
|
||||
labels <span style="color: #666666">=</span> to_categorical(labels)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># split into train and test data</span>
|
||||
<span style="color: #408080; font-style: italic"># one-liner from scikit-learn library</span>
|
||||
train_size <span style="color: #666666">=</span> <span style="color: #666666">0.8</span>
|
||||
test_size <span style="color: #666666">=</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> train_size
|
||||
X_train, X_test, Y_train, Y_test <span style="color: #666666">=</span> train_test_split(inputs, labels, train_size<span style="color: #666666">=</span>train_size,
|
||||
test_size<span style="color: #666666">=</span>test_size)
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -433,6 +440,8 @@ X_train, X_test, Y_train, Y_test <span style="color: #666666">=</span> train_tes
|
||||
<li><a href="._week42-bs081.html">82</a></li>
|
||||
<li><a href="._week42-bs082.html">83</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs075.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -379,40 +394,20 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0075"></a>
|
||||
<!-- !split -->
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="running-with-keras" class="anchor">Running with Keras </h2>
|
||||
<h2 id="systematic-reduction" class="anchor">Systematic reduction </h2>
|
||||
|
||||
<p>
|
||||
By systematically reducing the size of the input volume, through
|
||||
convolution and pooling, the network should create representations of
|
||||
small parts of the input, and then from them assemble representations
|
||||
of larger areas. The final pooling layer is flattened to serve as
|
||||
input to a hidden layer, such that each neuron in the final pooling
|
||||
layer is connected to every single neuron in the hidden layer. This
|
||||
then serves as input to the output layer, e.g. a softmax output for
|
||||
classification.
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_convolutional_neural_network_keras</span>(input_shape, receptive_field,
|
||||
n_filters, n_neurons_connected, n_categories,
|
||||
eta, lmbd):
|
||||
model <span style="color: #666666">=</span> Sequential()
|
||||
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Conv2D(n_filters, (receptive_field, receptive_field), input_shape<span style="color: #666666">=</span>input_shape, padding<span style="color: #666666">=</span><span style="color: #BA2121">'same'</span>,
|
||||
activation<span style="color: #666666">=</span><span style="color: #BA2121">'relu'</span>, kernel_regularizer<span style="color: #666666">=</span>regularizers<span style="color: #666666">.</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>MaxPooling2D(pool_size<span style="color: #666666">=</span>(<span style="color: #666666">2</span>, <span style="color: #666666">2</span>)))
|
||||
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Flatten())
|
||||
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Dense(n_neurons_connected, activation<span style="color: #666666">=</span><span style="color: #BA2121">'relu'</span>, kernel_regularizer<span style="color: #666666">=</span>regularizers<span style="color: #666666">.</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Dense(n_categories, activation<span style="color: #666666">=</span><span style="color: #BA2121">'softmax'</span>, kernel_regularizer<span style="color: #666666">=</span>regularizers<span style="color: #666666">.</span>l2(lmbd)))
|
||||
|
||||
sgd <span style="color: #666666">=</span> optimizers<span style="color: #666666">.</span>SGD(lr<span style="color: #666666">=</span>eta)
|
||||
model<span style="color: #666666">.</span>compile(loss<span style="color: #666666">=</span><span style="color: #BA2121">'categorical_crossentropy'</span>, optimizer<span style="color: #666666">=</span>sgd, metrics<span style="color: #666666">=</span>[<span style="color: #BA2121">'accuracy'</span>])
|
||||
|
||||
<span style="color: #008000; font-weight: bold">return</span> model
|
||||
|
||||
epochs <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
batch_size <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
input_shape <span style="color: #666666">=</span> X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">1</span>:<span style="color: #666666">4</span>]
|
||||
receptive_field <span style="color: #666666">=</span> <span style="color: #666666">3</span>
|
||||
n_filters <span style="color: #666666">=</span> <span style="color: #666666">10</span>
|
||||
n_neurons_connected <span style="color: #666666">=</span> <span style="color: #666666">50</span>
|
||||
n_categories <span style="color: #666666">=</span> <span style="color: #666666">10</span>
|
||||
|
||||
eta_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
|
||||
lmbd_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -437,6 +432,9 @@ lmbd_vals <span style="color: #666666">=</span> np<span style="color: #666666">.
|
||||
<li><a href="._week42-bs081.html">82</a></li>
|
||||
<li><a href="._week42-bs082.html">83</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs084.html">85</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs076.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -194,10 +194,14 @@ Automatically generated HTML file from DocOnce source
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -213,6 +217,14 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -343,29 +355,32 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs058.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs059.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs060.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs061.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs062.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs063.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs064.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs065.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs066.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs067.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs068.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs069.html#convolution-examples-probability-theory" style="font-size: 80%;">Convolution Examples: Probability Theory</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs070.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs071.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs072.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs073.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs074.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs075.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs076.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs077.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs078.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs079.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs080.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs081.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs082.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs083.html#set-up-the-model" style="font-size: 80%;">Set up the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs084.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs085.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week42-bs086.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -424,7 +439,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._week42-bs008.html">9</a></li>
|
||||
<li><a href="._week42-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week42-bs083.html">84</a></li>
|
||||
<li><a href="._week42-bs086.html">87</a></li>
|
||||
<li><a href="._week42-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -3226,13 +3226,98 @@ How can we use this? And what does it mean? Let us study some familiar examples
|
||||
<h2 id="convolution-examples-polynomial-multiplication">Convolution Examples: Polynomial multiplication </h2>
|
||||
|
||||
<p>
|
||||
We have already met such an example in project 1 when we tried to set up the design matrix for a two-dimensional function.
|
||||
Let us remind of this and recast it in terms of the mathematical operation of convolution.
|
||||
We have already met such an example in project 1 when we tried to set
|
||||
up the design matrix for a two-dimensional function. This was an
|
||||
example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.
|
||||
Let us look a the following polynomials to second and third order, respectively:
|
||||
<p> <br>
|
||||
$$
|
||||
p(t) = \alpha_0+\alpha_1 t+\alpha_2 t^2,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
and
|
||||
<p> <br>
|
||||
$$
|
||||
s(t) = \beta_0+\beta_1 t+\beta_2 t^2+\beta_3 t^3.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>
|
||||
The polynomial multiplication gives us a new polynomial of degree \( 5 \)
|
||||
<p> <br>
|
||||
$$
|
||||
z(t) = \delta_0+\delta_1 t+\delta_2 t^2+\delta_3 t^3+\delta_4 t^4+\delta_5 t^5.
|
||||
$$
|
||||
<p> <br>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="convolution-examples-probability-theory">Convolution Examples: Probability Theory </h2>
|
||||
<h2 id="efficient-polynomial-multiplication">Efficient Polynomial Multiplication </h2>
|
||||
|
||||
<p>
|
||||
Computing polynomial products can be implemented efficiently if we rewrite the the more brute force multiplications using convolution.
|
||||
We note first that the new coefficients are given as
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{split}
|
||||
\delta_0=&\alpha_0\beta_0\\
|
||||
\delta_1=&\alpha_1\beta_0+\beta_0\alpha_1\\
|
||||
\delta_2=&\alpha_0\beta_2+\beta_1\alpha_1+\alpha_2\beta_0\\
|
||||
\delta_3=&\alpha_1\beta_2+\beta_1\alpha_2+\alpha_0\beta_3\\
|
||||
\delta_4=&\alpha_2\beta_2+\beta_3\alpha_1\\
|
||||
\delta_5=&\alpha_2\beta_3.\\
|
||||
\end{split}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>
|
||||
We note that \( \alpha_i=0 \) except for \( i\in \left{0,1,2\right} \) and \( \beta_i=0 \) except for \( i\in\left{0,1,2,3\right} \).
|
||||
|
||||
<p>
|
||||
We can then rewrite the coefficients \( \delta_j \) using a discrete convolution as
|
||||
<p> <br>
|
||||
$$
|
||||
\delta_j = \sum_{i=-\infty}^{i=\infty}\alpha_i\beta_{j-i}=(\alpha * \beta)_j,
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
or as a double sum with restriction \( l=i+j \)
|
||||
<p> <br>
|
||||
$$
|
||||
\delta_l = \sum_{ij}\alpha_i\beta_{j}.
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>
|
||||
Do you see a potential drawback with these equations?
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="a-more-efficient-way-of-coding-the-above-convolution">A more efficient way of coding the above Convolution </h2>
|
||||
|
||||
<p>
|
||||
Since we only have a finite number of \( \alpha \) and \( \beta \) values
|
||||
which are non-zero, we can rewrite the above convolution expressions
|
||||
as a matrix-vector multiplication
|
||||
|
||||
<p> <br>
|
||||
$$
|
||||
\boldsymbol{\delta}=\begin{bmatriax}\alpha_0 & 0 & 0 & 0 \\
|
||||
\alpha_1 & \alpha_0 & 0 & 0 \\
|
||||
\alpha_2 & \alpha_1 & \alpha_0 & 0 \\
|
||||
0 & \alpha_2 & \alpha_1 & \alpha_0 \\
|
||||
0 & 0 & \alpha_2 & \alpha_1 \\
|
||||
0 & 0 & 0 & \alpha_2
|
||||
\end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3\end{bmatrix}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
<p>
|
||||
The process is commutative and we can easily see that we can rewrite the multiplication in terms of a martrix holding \( \beta \) and a vector holding \( \alpha \).
|
||||
</section>
|
||||
|
||||
|
||||
@@ -3243,7 +3328,7 @@ Let us remind of this and recast it in terms of the mathematical operation of co
|
||||
For problems with so-called harmonic oscillations, given by for example the following differential equation
|
||||
<p> <br>
|
||||
$$
|
||||
m\frac{d^2x(t)}(dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
@@ -3458,6 +3543,62 @@ The same method can be used to check for the consistency of \( g_n \).
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="final-words-on-fourier-transforms">Final words on Fourier Transforms </h2>
|
||||
|
||||
<p>
|
||||
The code here uses the Fourier series applied to a
|
||||
square wave signal. The code here
|
||||
visualizes the various approximations given by Fourier series compared
|
||||
with a square wave with period \( T=0.2 \) (dimensionless time), width \( 0.1 \) and max value of the force \( F=2 \). We
|
||||
see that when we increase the number of components in the Fourier
|
||||
series, the Fourier series approximation gets closer and closer to the
|
||||
square wave signal.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">math</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">scipy</span> <span style="color: #8B008B; font-weight: bold">import</span> signal
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
|
||||
|
||||
<span style="color: #228B22"># number of points </span>
|
||||
n = <span style="color: #B452CD">500</span>
|
||||
<span style="color: #228B22"># start and final times </span>
|
||||
t0 = <span style="color: #B452CD">0.0</span>
|
||||
tn = <span style="color: #B452CD">1.0</span>
|
||||
<span style="color: #228B22"># Period </span>
|
||||
T =<span style="color: #B452CD">0.2</span>
|
||||
<span style="color: #228B22"># Max value of square signal </span>
|
||||
Fmax= <span style="color: #B452CD">2.0</span>
|
||||
<span style="color: #228B22"># Width of signal </span>
|
||||
Width = <span style="color: #B452CD">0.1</span>
|
||||
t = np.linspace(t0, tn, n, endpoint=<span style="color: #8B008B; font-weight: bold">False</span>)
|
||||
SqrSignal = np.zeros(n)
|
||||
FourierSeriesSignal = np.zeros(n)
|
||||
SqrSignal = <span style="color: #B452CD">1.0</span>+signal.square(<span style="color: #B452CD">2</span>*np.pi*<span style="color: #B452CD">5</span>*t+np.pi*Width/T)
|
||||
a0 = Fmax*Width/T
|
||||
FourierSeriesSignal = a0
|
||||
Factor = <span style="color: #B452CD">2.0</span>*Fmax/np.pi
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #B452CD">1</span>,<span style="color: #B452CD">500</span>):
|
||||
FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*<span style="color: #B452CD">2</span>*np.pi/T)
|
||||
plt.plot(t, SqrSignal)
|
||||
plt.plot(t, FourierSeriesSignal)
|
||||
plt.ylim(-<span style="color: #B452CD">0.5</span>, <span style="color: #B452CD">2.5</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="convolution-examples-probability-theory">Convolution Examples: Probability Theory </h2>
|
||||
|
||||
<p>
|
||||
More text will be added here
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
|
||||
@@ -214,10 +214,14 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -233,6 +237,14 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -3239,13 +3251,84 @@ How can we use this? And what does it mean? Let us study some familiar examples
|
||||
<h2 id="convolution-examples-polynomial-multiplication">Convolution Examples: Polynomial multiplication </h2>
|
||||
|
||||
<p>
|
||||
We have already met such an example in project 1 when we tried to set up the design matrix for a two-dimensional function.
|
||||
Let us remind of this and recast it in terms of the mathematical operation of convolution.
|
||||
We have already met such an example in project 1 when we tried to set
|
||||
up the design matrix for a two-dimensional function. This was an
|
||||
example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.
|
||||
Let us look a the following polynomials to second and third order, respectively:
|
||||
$$
|
||||
p(t) = \alpha_0+\alpha_1 t+\alpha_2 t^2,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
s(t) = \beta_0+\beta_1 t+\beta_2 t^2+\beta_3 t^3.
|
||||
$$
|
||||
|
||||
<p>
|
||||
The polynomial multiplication gives us a new polynomial of degree \( 5 \)
|
||||
$$
|
||||
z(t) = \delta_0+\delta_1 t+\delta_2 t^2+\delta_3 t^3+\delta_4 t^4+\delta_5 t^5.
|
||||
$$
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="convolution-examples-probability-theory">Convolution Examples: Probability Theory </h2>
|
||||
<h2 id="efficient-polynomial-multiplication">Efficient Polynomial Multiplication </h2>
|
||||
|
||||
<p>
|
||||
Computing polynomial products can be implemented efficiently if we rewrite the the more brute force multiplications using convolution.
|
||||
We note first that the new coefficients are given as
|
||||
|
||||
$$
|
||||
\begin{split}
|
||||
\delta_0=&\alpha_0\beta_0\\
|
||||
\delta_1=&\alpha_1\beta_0+\beta_0\alpha_1\\
|
||||
\delta_2=&\alpha_0\beta_2+\beta_1\alpha_1+\alpha_2\beta_0\\
|
||||
\delta_3=&\alpha_1\beta_2+\beta_1\alpha_2+\alpha_0\beta_3\\
|
||||
\delta_4=&\alpha_2\beta_2+\beta_3\alpha_1\\
|
||||
\delta_5=&\alpha_2\beta_3.\\
|
||||
\end{split}
|
||||
$$
|
||||
|
||||
<p>
|
||||
We note that \( \alpha_i=0 \) except for \( i\in \left{0,1,2\right} \) and \( \beta_i=0 \) except for \( i\in\left{0,1,2,3\right} \).
|
||||
|
||||
<p>
|
||||
We can then rewrite the coefficients \( \delta_j \) using a discrete convolution as
|
||||
$$
|
||||
\delta_j = \sum_{i=-\infty}^{i=\infty}\alpha_i\beta_{j-i}=(\alpha * \beta)_j,
|
||||
$$
|
||||
|
||||
or as a double sum with restriction \( l=i+j \)
|
||||
$$
|
||||
\delta_l = \sum_{ij}\alpha_i\beta_{j}.
|
||||
$$
|
||||
|
||||
<p>
|
||||
Do you see a potential drawback with these equations?
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="a-more-efficient-way-of-coding-the-above-convolution">A more efficient way of coding the above Convolution </h2>
|
||||
|
||||
<p>
|
||||
Since we only have a finite number of \( \alpha \) and \( \beta \) values
|
||||
which are non-zero, we can rewrite the above convolution expressions
|
||||
as a matrix-vector multiplication
|
||||
|
||||
$$
|
||||
\boldsymbol{\delta}=\begin{bmatriax}\alpha_0 & 0 & 0 & 0 \\
|
||||
\alpha_1 & \alpha_0 & 0 & 0 \\
|
||||
\alpha_2 & \alpha_1 & \alpha_0 & 0 \\
|
||||
0 & \alpha_2 & \alpha_1 & \alpha_0 \\
|
||||
0 & 0 & \alpha_2 & \alpha_1 \\
|
||||
0 & 0 & 0 & \alpha_2
|
||||
\end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3\end{bmatrix}
|
||||
$$
|
||||
|
||||
<p>
|
||||
The process is commutative and we can easily see that we can rewrite the multiplication in terms of a martrix holding \( \beta \) and a vector holding \( \alpha \).
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
@@ -3255,7 +3338,7 @@ Let us remind of this and recast it in terms of the mathematical operation of co
|
||||
<p>
|
||||
For problems with so-called harmonic oscillations, given by for example the following differential equation
|
||||
$$
|
||||
m\frac{d^2x(t)}(dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
$$
|
||||
|
||||
where \( F(t) \) is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.
|
||||
@@ -3452,6 +3535,61 @@ The same method can be used to check for the consistency of \( g_n \).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="final-words-on-fourier-transforms">Final words on Fourier Transforms </h2>
|
||||
|
||||
<p>
|
||||
The code here uses the Fourier series applied to a
|
||||
square wave signal. The code here
|
||||
visualizes the various approximations given by Fourier series compared
|
||||
with a square wave with period \( T=0.2 \) (dimensionless time), width \( 0.1 \) and max value of the force \( F=2 \). We
|
||||
see that when we increase the number of components in the Fourier
|
||||
series, the Fourier series approximation gets closer and closer to the
|
||||
square wave signal.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">math</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">scipy</span> <span style="color: #8B008B; font-weight: bold">import</span> signal
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
|
||||
|
||||
<span style="color: #228B22"># number of points </span>
|
||||
n = <span style="color: #B452CD">500</span>
|
||||
<span style="color: #228B22"># start and final times </span>
|
||||
t0 = <span style="color: #B452CD">0.0</span>
|
||||
tn = <span style="color: #B452CD">1.0</span>
|
||||
<span style="color: #228B22"># Period </span>
|
||||
T =<span style="color: #B452CD">0.2</span>
|
||||
<span style="color: #228B22"># Max value of square signal </span>
|
||||
Fmax= <span style="color: #B452CD">2.0</span>
|
||||
<span style="color: #228B22"># Width of signal </span>
|
||||
Width = <span style="color: #B452CD">0.1</span>
|
||||
t = np.linspace(t0, tn, n, endpoint=<span style="color: #8B008B; font-weight: bold">False</span>)
|
||||
SqrSignal = np.zeros(n)
|
||||
FourierSeriesSignal = np.zeros(n)
|
||||
SqrSignal = <span style="color: #B452CD">1.0</span>+signal.square(<span style="color: #B452CD">2</span>*np.pi*<span style="color: #B452CD">5</span>*t+np.pi*Width/T)
|
||||
a0 = Fmax*Width/T
|
||||
FourierSeriesSignal = a0
|
||||
Factor = <span style="color: #B452CD">2.0</span>*Fmax/np.pi
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #B452CD">1</span>,<span style="color: #B452CD">500</span>):
|
||||
FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*<span style="color: #B452CD">2</span>*np.pi/T)
|
||||
plt.plot(t, SqrSignal)
|
||||
plt.plot(t, FourierSeriesSignal)
|
||||
plt.ylim(-<span style="color: #B452CD">0.5</span>, <span style="color: #B452CD">2.5</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="convolution-examples-probability-theory">Convolution Examples: Probability Theory </h2>
|
||||
|
||||
<p>
|
||||
More text will be added here
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
<p>
|
||||
|
||||
@@ -219,10 +219,14 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-polynomial-multiplication'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
('Efficient Polynomial Multiplication',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
'efficient-polynomial-multiplication'),
|
||||
('A more efficient way of coding the above Convolution',
|
||||
2,
|
||||
None,
|
||||
'a-more-efficient-way-of-coding-the-above-convolution'),
|
||||
('Convolution Examples: Principle of Superposition and Periodic '
|
||||
'Forces (Fourier Transforms)',
|
||||
2,
|
||||
@@ -238,6 +242,14 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'wrapping-up-fourier-transforms'),
|
||||
('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
|
||||
('Final words on Fourier Transforms',
|
||||
2,
|
||||
None,
|
||||
'final-words-on-fourier-transforms'),
|
||||
('Convolution Examples: Probability Theory',
|
||||
2,
|
||||
None,
|
||||
'convolution-examples-probability-theory'),
|
||||
('CNNs in more detail, building convolutional neural networks in '
|
||||
'Tensorflow and Keras',
|
||||
2,
|
||||
@@ -3244,13 +3256,84 @@ How can we use this? And what does it mean? Let us study some familiar examples
|
||||
<h2 id="convolution-examples-polynomial-multiplication">Convolution Examples: Polynomial multiplication </h2>
|
||||
|
||||
<p>
|
||||
We have already met such an example in project 1 when we tried to set up the design matrix for a two-dimensional function.
|
||||
Let us remind of this and recast it in terms of the mathematical operation of convolution.
|
||||
We have already met such an example in project 1 when we tried to set
|
||||
up the design matrix for a two-dimensional function. This was an
|
||||
example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.
|
||||
Let us look a the following polynomials to second and third order, respectively:
|
||||
$$
|
||||
p(t) = \alpha_0+\alpha_1 t+\alpha_2 t^2,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
s(t) = \beta_0+\beta_1 t+\beta_2 t^2+\beta_3 t^3.
|
||||
$$
|
||||
|
||||
<p>
|
||||
The polynomial multiplication gives us a new polynomial of degree \( 5 \)
|
||||
$$
|
||||
z(t) = \delta_0+\delta_1 t+\delta_2 t^2+\delta_3 t^3+\delta_4 t^4+\delta_5 t^5.
|
||||
$$
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="convolution-examples-probability-theory">Convolution Examples: Probability Theory </h2>
|
||||
<h2 id="efficient-polynomial-multiplication">Efficient Polynomial Multiplication </h2>
|
||||
|
||||
<p>
|
||||
Computing polynomial products can be implemented efficiently if we rewrite the the more brute force multiplications using convolution.
|
||||
We note first that the new coefficients are given as
|
||||
|
||||
$$
|
||||
\begin{split}
|
||||
\delta_0=&\alpha_0\beta_0\\
|
||||
\delta_1=&\alpha_1\beta_0+\beta_0\alpha_1\\
|
||||
\delta_2=&\alpha_0\beta_2+\beta_1\alpha_1+\alpha_2\beta_0\\
|
||||
\delta_3=&\alpha_1\beta_2+\beta_1\alpha_2+\alpha_0\beta_3\\
|
||||
\delta_4=&\alpha_2\beta_2+\beta_3\alpha_1\\
|
||||
\delta_5=&\alpha_2\beta_3.\\
|
||||
\end{split}
|
||||
$$
|
||||
|
||||
<p>
|
||||
We note that \( \alpha_i=0 \) except for \( i\in \left{0,1,2\right} \) and \( \beta_i=0 \) except for \( i\in\left{0,1,2,3\right} \).
|
||||
|
||||
<p>
|
||||
We can then rewrite the coefficients \( \delta_j \) using a discrete convolution as
|
||||
$$
|
||||
\delta_j = \sum_{i=-\infty}^{i=\infty}\alpha_i\beta_{j-i}=(\alpha * \beta)_j,
|
||||
$$
|
||||
|
||||
or as a double sum with restriction \( l=i+j \)
|
||||
$$
|
||||
\delta_l = \sum_{ij}\alpha_i\beta_{j}.
|
||||
$$
|
||||
|
||||
<p>
|
||||
Do you see a potential drawback with these equations?
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="a-more-efficient-way-of-coding-the-above-convolution">A more efficient way of coding the above Convolution </h2>
|
||||
|
||||
<p>
|
||||
Since we only have a finite number of \( \alpha \) and \( \beta \) values
|
||||
which are non-zero, we can rewrite the above convolution expressions
|
||||
as a matrix-vector multiplication
|
||||
|
||||
$$
|
||||
\boldsymbol{\delta}=\begin{bmatriax}\alpha_0 & 0 & 0 & 0 \\
|
||||
\alpha_1 & \alpha_0 & 0 & 0 \\
|
||||
\alpha_2 & \alpha_1 & \alpha_0 & 0 \\
|
||||
0 & \alpha_2 & \alpha_1 & \alpha_0 \\
|
||||
0 & 0 & \alpha_2 & \alpha_1 \\
|
||||
0 & 0 & 0 & \alpha_2
|
||||
\end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3\end{bmatrix}
|
||||
$$
|
||||
|
||||
<p>
|
||||
The process is commutative and we can easily see that we can rewrite the multiplication in terms of a martrix holding \( \beta \) and a vector holding \( \alpha \).
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
@@ -3260,7 +3343,7 @@ Let us remind of this and recast it in terms of the mathematical operation of co
|
||||
<p>
|
||||
For problems with so-called harmonic oscillations, given by for example the following differential equation
|
||||
$$
|
||||
m\frac{d^2x(t)}(dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
$$
|
||||
|
||||
where \( F(t) \) is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.
|
||||
@@ -3457,6 +3540,61 @@ The same method can be used to check for the consistency of \( g_n \).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="final-words-on-fourier-transforms">Final words on Fourier Transforms </h2>
|
||||
|
||||
<p>
|
||||
The code here uses the Fourier series applied to a
|
||||
square wave signal. The code here
|
||||
visualizes the various approximations given by Fourier series compared
|
||||
with a square wave with period \( T=0.2 \) (dimensionless time), width \( 0.1 \) and max value of the force \( F=2 \). We
|
||||
see that when we increase the number of components in the Fourier
|
||||
series, the Fourier series approximation gets closer and closer to the
|
||||
square wave signal.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">math</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">scipy</span> <span style="color: #008000; font-weight: bold">import</span> signal
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
|
||||
<span style="color: #408080; font-style: italic"># number of points </span>
|
||||
n <span style="color: #666666">=</span> <span style="color: #666666">500</span>
|
||||
<span style="color: #408080; font-style: italic"># start and final times </span>
|
||||
t0 <span style="color: #666666">=</span> <span style="color: #666666">0.0</span>
|
||||
tn <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
|
||||
<span style="color: #408080; font-style: italic"># Period </span>
|
||||
T <span style="color: #666666">=0.2</span>
|
||||
<span style="color: #408080; font-style: italic"># Max value of square signal </span>
|
||||
Fmax<span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
|
||||
<span style="color: #408080; font-style: italic"># Width of signal </span>
|
||||
Width <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
|
||||
t <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(t0, tn, n, endpoint<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>)
|
||||
SqrSignal <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(n)
|
||||
FourierSeriesSignal <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(n)
|
||||
SqrSignal <span style="color: #666666">=</span> <span style="color: #666666">1.0+</span>signal<span style="color: #666666">.</span>square(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*5*</span>t<span style="color: #666666">+</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>Width<span style="color: #666666">/</span>T)
|
||||
a0 <span style="color: #666666">=</span> Fmax<span style="color: #666666">*</span>Width<span style="color: #666666">/</span>T
|
||||
FourierSeriesSignal <span style="color: #666666">=</span> a0
|
||||
Factor <span style="color: #666666">=</span> <span style="color: #666666">2.0*</span>Fmax<span style="color: #666666">/</span>np<span style="color: #666666">.</span>pi
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,<span style="color: #666666">500</span>):
|
||||
FourierSeriesSignal <span style="color: #666666">+=</span> Factor<span style="color: #666666">/</span>(i)<span style="color: #666666">*</span>np<span style="color: #666666">.</span>sin(np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>i<span style="color: #666666">*</span>Width<span style="color: #666666">/</span>T)<span style="color: #666666">*</span>np<span style="color: #666666">.</span>cos(i<span style="color: #666666">*</span>t<span style="color: #666666">*2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">/</span>T)
|
||||
plt<span style="color: #666666">.</span>plot(t, SqrSignal)
|
||||
plt<span style="color: #666666">.</span>plot(t, FourierSeriesSignal)
|
||||
plt<span style="color: #666666">.</span>ylim(<span style="color: #666666">-0.5</span>, <span style="color: #666666">2.5</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="convolution-examples-probability-theory">Convolution Examples: Probability Theory </h2>
|
||||
|
||||
<p>
|
||||
More text will be added here
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
<p>
|
||||
|
||||
Binary file not shown.
@@ -3350,16 +3350,150 @@
|
||||
"\n",
|
||||
"## Convolution Examples: Polynomial multiplication\n",
|
||||
"\n",
|
||||
"We have already met such an example in project 1 when we tried to set up the design matrix for a two-dimensional function.\n",
|
||||
"Let us remind of this and recast it in terms of the mathematical operation of convolution.\n",
|
||||
"We have already met such an example in project 1 when we tried to set\n",
|
||||
"up the design matrix for a two-dimensional function. This was an\n",
|
||||
"example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.\n",
|
||||
"Let us look a the following polynomials to second and third order, respectively:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"p(t) = \\alpha_0+\\alpha_1 t+\\alpha_2 t^2,\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"s(t) = \\beta_0+\\beta_1 t+\\beta_2 t^2+\\beta_3 t^3.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The polynomial multiplication gives us a new polynomial of degree $5$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"z(t) = \\delta_0+\\delta_1 t+\\delta_2 t^2+\\delta_3 t^3+\\delta_4 t^4+\\delta_5 t^5.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Efficient Polynomial Multiplication\n",
|
||||
"\n",
|
||||
"Computing polynomial products can be implemented efficiently if we rewrite the the more brute force multiplications using convolution.\n",
|
||||
"We note first that the new coefficients are given as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\begin{split}\n",
|
||||
"\\delta_0=&\\alpha_0\\beta_0\\\\\n",
|
||||
"\\delta_1=&\\alpha_1\\beta_0+\\beta_0\\alpha_1\\\\\n",
|
||||
"\\delta_2=&\\alpha_0\\beta_2+\\beta_1\\alpha_1+\\alpha_2\\beta_0\\\\\n",
|
||||
"\\delta_3=&\\alpha_1\\beta_2+\\beta_1\\alpha_2+\\alpha_0\\beta_3\\\\\n",
|
||||
"\\delta_4=&\\alpha_2\\beta_2+\\beta_3\\alpha_1\\\\\n",
|
||||
"\\delta_5=&\\alpha_2\\beta_3.\\\\\n",
|
||||
"\\end{split}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We note that $\\alpha_i=0$ except for $i\\in \\left{0,1,2\\right}$ and $\\beta_i=0$ except for $i\\in\\left{0,1,2,3\\right}$.\n",
|
||||
"\n",
|
||||
"We can then rewrite the coefficients $\\delta_j$ using a discrete convolution as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\delta_j = \\sum_{i=-\\infty}^{i=\\infty}\\alpha_i\\beta_{j-i}=(\\alpha * \\beta)_j,\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"or as a double sum with restriction $l=i+j$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\delta_l = \\sum_{ij}\\alpha_i\\beta_{j}.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Do you see a potential drawback with these equations?\n",
|
||||
"\n",
|
||||
"## A more efficient way of coding the above Convolution\n",
|
||||
"\n",
|
||||
"Since we only have a finite number of $\\alpha$ and $\\beta$ values\n",
|
||||
"which are non-zero, we can rewrite the above convolution expressions\n",
|
||||
"as a matrix-vector multiplication"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\boldsymbol{\\delta}=\\begin{bmatriax}\\alpha_0 & 0 & 0 & 0 \\\\\n",
|
||||
" \\alpha_1 & \\alpha_0 & 0 & 0 \\\\\n",
|
||||
"\t\t\t \\alpha_2 & \\alpha_1 & \\alpha_0 & 0 \\\\\n",
|
||||
"\t\t\t 0 & \\alpha_2 & \\alpha_1 & \\alpha_0 \\\\\n",
|
||||
"\t\t\t 0 & 0 & \\alpha_2 & \\alpha_1 \\\\\n",
|
||||
"\t\t\t 0 & 0 & 0 & \\alpha_2\n",
|
||||
"\t\t\t \\end{bmatrix}\\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\beta_3\\end{bmatrix}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The process is commutative and we can easily see that we can rewrite the multiplication in terms of a martrix holding $\\beta$ and a vector holding $\\alpha$.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## Convolution Examples: Probability Theory\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)\n",
|
||||
"\n",
|
||||
"For problems with so-called harmonic oscillations, given by for example the following differential equation"
|
||||
@@ -3370,7 +3504,7 @@
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"m\\frac{d^2x(t)}(dt^2}+\\eta\\frac{dx}{dt}+x(t)=F(t),\n",
|
||||
"m\\frac{d^2x}{dt^2}+\\eta\\frac{dx}{dt}+x(t)=F(t),\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
@@ -3662,8 +3796,64 @@
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## Final words on Fourier Transforms\n",
|
||||
"\n",
|
||||
"The code here uses the Fourier series applied to a \n",
|
||||
"square wave signal. The code here\n",
|
||||
"visualizes the various approximations given by Fourier series compared\n",
|
||||
"with a square wave with period $T=0.2$ (dimensionless time), width $0.1$ and max value of the force $F=2$. We\n",
|
||||
"see that when we increase the number of components in the Fourier\n",
|
||||
"series, the Fourier series approximation gets closer and closer to the\n",
|
||||
"square wave signal."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import numpy as np\n",
|
||||
"import math\n",
|
||||
"from scipy import signal\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"\n",
|
||||
"# number of points \n",
|
||||
"n = 500\n",
|
||||
"# start and final times \n",
|
||||
"t0 = 0.0\n",
|
||||
"tn = 1.0\n",
|
||||
"# Period \n",
|
||||
"T =0.2\n",
|
||||
"# Max value of square signal \n",
|
||||
"Fmax= 2.0\n",
|
||||
"# Width of signal \n",
|
||||
"Width = 0.1\n",
|
||||
"t = np.linspace(t0, tn, n, endpoint=False)\n",
|
||||
"SqrSignal = np.zeros(n)\n",
|
||||
"FourierSeriesSignal = np.zeros(n)\n",
|
||||
"SqrSignal = 1.0+signal.square(2*np.pi*5*t+np.pi*Width/T)\n",
|
||||
"a0 = Fmax*Width/T\n",
|
||||
"FourierSeriesSignal = a0\n",
|
||||
"Factor = 2.0*Fmax/np.pi\n",
|
||||
"for i in range(1,500):\n",
|
||||
" FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*2*np.pi/T)\n",
|
||||
"plt.plot(t, SqrSignal)\n",
|
||||
"plt.plot(t, FourierSeriesSignal)\n",
|
||||
"plt.ylim(-0.5, 2.5)\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Convolution Examples: Probability Theory\n",
|
||||
"\n",
|
||||
"More text will be added here\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
|
||||
@@ -2637,15 +2637,86 @@ How can we use this? And what does it mean? Let us study some familiar examples
|
||||
!split
|
||||
===== Convolution Examples: Polynomial multiplication =====
|
||||
|
||||
We have already met such an example in project 1 when we tried to set up the design matrix for a two-dimensional function.
|
||||
Let us remind of this and recast it in terms of the mathematical operation of convolution.
|
||||
|
||||
|
||||
|
||||
We have already met such an example in project 1 when we tried to set
|
||||
up the design matrix for a two-dimensional function. This was an
|
||||
example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.
|
||||
Let us look a the following polynomials to second and third order, respectively:
|
||||
!bt
|
||||
\[
|
||||
p(t) = \alpha_0+\alpha_1 t+\alpha_2 t^2,
|
||||
\]
|
||||
!et
|
||||
and
|
||||
!bt
|
||||
\[
|
||||
s(t) = \beta_0+\beta_1 t+\beta_2 t^2+\beta_3 t^3.
|
||||
\]
|
||||
!et
|
||||
|
||||
The polynomial multiplication gives us a new polynomial of degree $5$
|
||||
!bt
|
||||
\[
|
||||
z(t) = \delta_0+\delta_1 t+\delta_2 t^2+\delta_3 t^3+\delta_4 t^4+\delta_5 t^5.
|
||||
\]
|
||||
!et
|
||||
|
||||
!split
|
||||
===== Convolution Examples: Probability Theory =====
|
||||
===== Efficient Polynomial Multiplication =====
|
||||
|
||||
Computing polynomial products can be implemented efficiently if we rewrite the the more brute force multiplications using convolution.
|
||||
We note first that the new coefficients are given as
|
||||
|
||||
!bt
|
||||
\begin{split}
|
||||
\delta_0=&\alpha_0\beta_0\\
|
||||
\delta_1=&\alpha_1\beta_0+\beta_0\alpha_1\\
|
||||
\delta_2=&\alpha_0\beta_2+\beta_1\alpha_1+\alpha_2\beta_0\\
|
||||
\delta_3=&\alpha_1\beta_2+\beta_1\alpha_2+\alpha_0\beta_3\\
|
||||
\delta_4=&\alpha_2\beta_2+\beta_3\alpha_1\\
|
||||
\delta_5=&\alpha_2\beta_3.\\
|
||||
\end{split}
|
||||
!et
|
||||
|
||||
|
||||
We note that $\alpha_i=0$ except for $i\in \left{0,1,2\right}$ and $\beta_i=0$ except for $i\in\left{0,1,2,3\right}$.
|
||||
|
||||
We can then rewrite the coefficients $\delta_j$ using a discrete convolution as
|
||||
!bt
|
||||
\[
|
||||
\delta_j = \sum_{i=-\infty}^{i=\infty}\alpha_i\beta_{j-i}=(\alpha * \beta)_j,
|
||||
\]
|
||||
!et
|
||||
or as a double sum with restriction $l=i+j$
|
||||
!bt
|
||||
\[
|
||||
\delta_l = \sum_{ij}\alpha_i\beta_{j}.
|
||||
\]
|
||||
!et
|
||||
|
||||
Do you see a potential drawback with these equations?
|
||||
|
||||
!split
|
||||
===== A more efficient way of coding the above Convolution =====
|
||||
|
||||
Since we only have a finite number of $\alpha$ and $\beta$ values
|
||||
which are non-zero, we can rewrite the above convolution expressions
|
||||
as a matrix-vector multiplication
|
||||
|
||||
!bt
|
||||
\[
|
||||
\bm{\delta}=\begin{bmatriax}\alpha_0 & 0 & 0 & 0 \\
|
||||
\alpha_1 & \alpha_0 & 0 & 0 \\
|
||||
\alpha_2 & \alpha_1 & \alpha_0 & 0 \\
|
||||
0 & \alpha_2 & \alpha_1 & \alpha_0 \\
|
||||
0 & 0 & \alpha_2 & \alpha_1 \\
|
||||
0 & 0 & 0 & \alpha_2
|
||||
\end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3\end{bmatrix}
|
||||
\]
|
||||
!et
|
||||
|
||||
The process is commutative and we can easily see that we can rewrite the multiplication in terms of a martrix holding $\beta$ and a vector holding $\alpha$.
|
||||
|
||||
|
||||
|
||||
|
||||
!split
|
||||
@@ -2654,7 +2725,7 @@ Let us remind of this and recast it in terms of the mathematical operation of co
|
||||
For problems with so-called harmonic oscillations, given by for example the following differential equation
|
||||
!bt
|
||||
\[
|
||||
m\frac{d^2x(t)}(dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t),
|
||||
\]
|
||||
!et
|
||||
where $F(t)$ is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.
|
||||
@@ -2825,8 +2896,54 @@ The same method can be used to check for the consistency of $g_n$.
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Final words on Fourier Transforms =====
|
||||
|
||||
The code here uses the Fourier series applied to a
|
||||
square wave signal. The code here
|
||||
visualizes the various approximations given by Fourier series compared
|
||||
with a square wave with period $T=0.2$ (dimensionless time), width $0.1$ and max value of the force $F=2$. We
|
||||
see that when we increase the number of components in the Fourier
|
||||
series, the Fourier series approximation gets closer and closer to the
|
||||
square wave signal.
|
||||
|
||||
!bc pycod
|
||||
import numpy as np
|
||||
import math
|
||||
from scipy import signal
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
# number of points
|
||||
n = 500
|
||||
# start and final times
|
||||
t0 = 0.0
|
||||
tn = 1.0
|
||||
# Period
|
||||
T =0.2
|
||||
# Max value of square signal
|
||||
Fmax= 2.0
|
||||
# Width of signal
|
||||
Width = 0.1
|
||||
t = np.linspace(t0, tn, n, endpoint=False)
|
||||
SqrSignal = np.zeros(n)
|
||||
FourierSeriesSignal = np.zeros(n)
|
||||
SqrSignal = 1.0+signal.square(2*np.pi*5*t+np.pi*Width/T)
|
||||
a0 = Fmax*Width/T
|
||||
FourierSeriesSignal = a0
|
||||
Factor = 2.0*Fmax/np.pi
|
||||
for i in range(1,500):
|
||||
FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*2*np.pi/T)
|
||||
plt.plot(t, SqrSignal)
|
||||
plt.plot(t, FourierSeriesSignal)
|
||||
plt.ylim(-0.5, 2.5)
|
||||
plt.show()
|
||||
!ec
|
||||
|
||||
|
||||
!split
|
||||
===== Convolution Examples: Probability Theory =====
|
||||
|
||||
More text will be added here
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user