mhjensen
275 lines
13 KiB
HTML
275 lines
13 KiB
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week42-bs001.html#___sec0" style="font-size: 80%;">Plan for week 42</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs002.html#___sec1" style="font-size: 80%;">Convolutional Neural Networks (recognizing images)</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs003.html#___sec2" style="font-size: 80%;">Neural Networks vs CNNs</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs004.html#___sec3" style="font-size: 80%;">Why CNNS for images, sound files, medical images from CT scans etc?</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs005.html#___sec4" style="font-size: 80%;">Regular NNs don’t scale well to full images</a></li>
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<!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;">3D volumes of neurons</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs007.html#___sec6" style="font-size: 80%;">Layers used to build CNNs</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs008.html#___sec7" style="font-size: 80%;">Transforming images</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs009.html#___sec8" style="font-size: 80%;">CNNs in brief</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs010.html#___sec9" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs011.html#___sec10" style="font-size: 80%;">Setting it up</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs012.html#___sec11" style="font-size: 80%;">The MNIST dataset again</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs013.html#___sec12" style="font-size: 80%;">Strong correlations</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs014.html#___sec13" style="font-size: 80%;">Layers of a CNN</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs015.html#___sec14" style="font-size: 80%;">Systematic reduction</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs016.html#___sec15" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs017.html#___sec16" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs018.html#___sec17" style="font-size: 80%;">Running with Keras</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs019.html#___sec18" style="font-size: 80%;">Final part</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs020.html#___sec19" style="font-size: 80%;">Final visualization</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs021.html#___sec20" style="font-size: 80%;">The CIFAR01 data set</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs022.html#___sec21" style="font-size: 80%;">Verifying the data set</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs023.html#___sec22" style="font-size: 80%;">Set up the model</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs024.html#___sec23" style="font-size: 80%;">Add Dense layers on top</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs025.html#___sec24" style="font-size: 80%;">Compile and train the model</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs026.html#___sec25" style="font-size: 80%;">Finally, evaluate the model</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs027.html#___sec26" style="font-size: 80%;">Recurrent neural networks: Overarching view</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs028.html#___sec27" style="font-size: 80%;">Set up of an RNN</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs029.html#___sec28" style="font-size: 80%;">A simple example</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs030.html#___sec29" style="font-size: 80%;">An extrapolation example</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs031.html#___sec30" style="font-size: 80%;">Formatting the Data</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs032.html#___sec31" style="font-size: 80%;">Predicting New Points With A Trained Recurrent Neural Network</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs033.html#___sec32" style="font-size: 80%;">Other Things to Try</a></li>
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<!-- navigation toc: --> <li><a href="._week42-bs034.html#___sec33" style="font-size: 80%;">Other Types of Recurrent Neural Networks</a></li>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0006"></a>
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<!-- !split -->
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<h2 id="___sec5" class="anchor">3D volumes of neurons </h2>
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<p>
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Convolutional Neural Networks take advantage of the fact that the
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input consists of images and they constrain the architecture in a more
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sensible way.
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<p>
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In particular, unlike a regular Neural Network, the
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layers of a CNN have neurons arranged in 3 dimensions: width,
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height, depth. (Note that the word depth here refers to the third
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dimension of an activation volume, not to the depth of a full Neural
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Network, which can refer to the total number of layers in a network.)
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<p>
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To understand it better, the above example of an image
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with an input volume of
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activations has dimensions \( 32\times 32\times 3 \) (width, height,
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depth respectively).
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<p>
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The neurons in a layer will
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only be connected to a small region of the layer before it, instead of
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all of the neurons in a fully-connected manner. Moreover, the final
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output layer could for this specific image have dimensions \( 1\times 1 \times 10 \),
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because by the
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end of the CNN architecture we will reduce the full image into a
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single vector of class scores, arranged along the depth
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dimension.
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<p>
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<center> <!-- FIGURE -->
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<hr class="figure">
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<center><p class="caption">Figure 2: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels). </p></center>
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<p><img src="figslides/cnn.jpeg" align="bottom" width=500></p>
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