Morten Hjorth-Jensen
410 lines
27 KiB
HTML
410 lines
27 KiB
HTML
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<title>Week 44, Convolutional Neural Networks (CNN)</title>
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<!-- tocinfo
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{'highest level': 2,
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'sections': [('Plan for week 44', 2, None, 'plan-for-week-44'),
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('Lab sessions on Tuesday and Wednesday',
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2,
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None,
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'lab-sessions-on-tuesday-and-wednesday'),
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('Material for Lecture Monday October 28',
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2,
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('Convolutional Neural Networks (recognizing images)',
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2,
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None,
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'convolutional-neural-networks-recognizing-images'),
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('What is the Difference', 2, None, 'what-is-the-difference'),
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('Neural Networks vs CNNs', 2, None, 'neural-networks-vs-cnns'),
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('Why CNNS for images, sound files, medical images from CT scans '
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'etc?',
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2,
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None,
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('3D volumes of neurons', 2, None, '3d-volumes-of-neurons'),
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('More on Dimensionalities', 2, None, 'more-on-dimensionalities'),
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('Further remarks', 2, None, 'further-remarks'),
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('Layers used to build CNNs',
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('Transforming images', 2, None, 'transforming-images'),
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('A deep CNN model ("From Raschka et '
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('How to do image compression before the era of deep learning',
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('The SVD example', 2, None, 'the-svd-example'),
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('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
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('Convolution Examples: Polynomial multiplication',
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2,
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None,
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'convolution-examples-polynomial-multiplication'),
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('Efficient Polynomial Multiplication',
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2,
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None,
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'efficient-polynomial-multiplication'),
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('Further simplification', 2, None, 'further-simplification'),
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('A more efficient way of coding the above Convolution',
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2,
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None,
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'a-more-efficient-way-of-coding-the-above-convolution'),
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('Commutative process', 2, None, 'commutative-process'),
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('Toeplitz matrices', 2, None, 'toeplitz-matrices'),
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('Fourier series and Toeplitz matrices',
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2,
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None,
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'fourier-series-and-toeplitz-matrices'),
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('Generalizing the above one-dimensional case',
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2,
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None,
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'generalizing-the-above-one-dimensional-case'),
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('Memory considerations', 2, None, 'memory-considerations'),
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('Padding', 2, None, 'padding'),
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('New vector', 2, None, 'new-vector'),
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('Rewriting as dot products',
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2,
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'rewriting-as-dot-products'),
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('Cross correlation', 2, None, 'cross-correlation'),
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('Two-dimensional objects', 2, None, 'two-dimensional-objects'),
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('CNNs in more detail, simple example',
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2,
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None,
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'cnns-in-more-detail-simple-example'),
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('The convolution stage', 2, None, 'the-convolution-stage'),
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('Finding the number of parameters',
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2,
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None,
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'finding-the-number-of-parameters'),
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('New image (or volume)', 2, None, 'new-image-or-volume'),
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('Parameters to train, common settings',
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2,
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None,
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'parameters-to-train-common-settings'),
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('Examples of CNN setups', 2, None, 'examples-of-cnn-setups'),
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('Summarizing: Performing a general discrete convolution ("From '
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'Raschka et '
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'al":"https://github.com/rasbt/machine-learning-book")',
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2,
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None,
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'summarizing-performing-a-general-discrete-convolution-from-raschka-et-al-https-github-com-rasbt-machine-learning-book'),
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('Pooling', 2, None, 'pooling'),
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('Pooling arithmetic', 2, None, 'pooling-arithmetic'),
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('Pooling types ("From Raschka et '
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'al":"https://github.com/rasbt/machine-learning-book")',
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2,
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None,
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'pooling-types-from-raschka-et-al-https-github-com-rasbt-machine-learning-book'),
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('Building convolutional neural networks in Tensorflow and Keras',
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2,
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None,
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'building-convolutional-neural-networks-in-tensorflow-and-keras'),
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('Setting it up', 2, None, 'setting-it-up'),
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('The MNIST dataset again', 2, None, 'the-mnist-dataset-again'),
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('Strong correlations', 2, None, 'strong-correlations'),
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('Layers of a CNN', 2, None, 'layers-of-a-cnn'),
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('Systematic reduction', 2, None, 'systematic-reduction'),
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('Prerequisites: Collect and pre-process data',
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2,
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None,
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'prerequisites-collect-and-pre-process-data'),
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('Importing Keras and Tensorflow',
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2,
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None,
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'importing-keras-and-tensorflow'),
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('Running with Keras', 2, None, 'running-with-keras'),
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('Final part', 2, None, 'final-part'),
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('Final visualization', 2, None, 'final-visualization'),
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('The CIFAR01 data set', 2, None, 'the-cifar01-data-set'),
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('Verifying the data set', 2, None, 'verifying-the-data-set'),
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('Set up the model', 2, None, 'set-up-the-model'),
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('Add Dense layers on top', 2, None, 'add-dense-layers-on-top'),
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('Compile and train the model',
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2,
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('Finally, evaluate the model',
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2,
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'finally-evaluate-the-model'),
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('Building our own CNN code',
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2,
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'building-our-own-cnn-code'),
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('List of contents:', 3, None, 'list-of-contents'),
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('Schedulers', 3, None, 'schedulers'),
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('Usage of schedulers', 3, None, 'usage-of-schedulers'),
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('Cost functions', 3, None, 'cost-functions'),
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('Usage of cost functions', 3, None, 'usage-of-cost-functions'),
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('Activation functions', 3, None, 'activation-functions'),
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('Usage of activation functions',
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3,
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None,
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'usage-of-activation-functions'),
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('Convolution', 3, None, 'convolution'),
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('Layers', 3, None, 'layers'),
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('Convolution2DLayer: convolution in a hidden layer',
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3,
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None,
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'convolution2dlayer-convolution-in-a-hidden-layer'),
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('Backpropagation in the convolutional layer',
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3,
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None,
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'backpropagation-in-the-convolutional-layer'),
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('Demonstration', 3, None, 'demonstration'),
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('Pooling Layer', 3, None, 'pooling-layer'),
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('Flattening Layer', 3, None, 'flattening-layer'),
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('Fully Connected Layers', 3, None, 'fully-connected-layers'),
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('Optimized Convolution2DLayer',
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3,
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None,
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'optimized-convolution2dlayer'),
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('The Convolutional Neural Network (CNN)',
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3,
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None,
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'the-convolutional-neural-network-cnn'),
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('Usage of CNN code', 3, None, 'usage-of-cnn-code'),
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('Additional Remarks', 3, None, 'additional-remarks'),
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('Remarks on the speed', 3, None, 'remarks-on-the-speed'),
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('Convolution using separable kernels',
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3,
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None,
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'convolution-using-separable-kernels'),
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('Convolution in the Fourier domain',
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3,
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None,
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'convolution-in-the-fourier-domain')]}
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<a class="navbar-brand" href="week44-bs.html">Week 44, Convolutional Neural Networks (CNN)</a>
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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="._week44-bs001.html#plan-for-week-44" style="font-size: 80%;"><b>Plan for week 44</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs002.html#lab-sessions-on-tuesday-and-wednesday" style="font-size: 80%;"><b>Lab sessions on Tuesday and Wednesday</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs003.html#material-for-lecture-monday-october-28" style="font-size: 80%;"><b>Material for Lecture Monday October 28</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs004.html#convolutional-neural-networks-recognizing-images" style="font-size: 80%;"><b>Convolutional Neural Networks (recognizing images)</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs005.html#what-is-the-difference" style="font-size: 80%;"><b>What is the Difference</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs006.html#neural-networks-vs-cnns" style="font-size: 80%;"><b>Neural Networks vs CNNs</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs007.html#why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc" style="font-size: 80%;"><b>Why CNNS for images, sound files, medical images from CT scans etc?</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs008.html#regular-nns-don-t-scale-well-to-full-images" style="font-size: 80%;"><b>Regular NNs don’t scale well to full images</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs009.html#3d-volumes-of-neurons" style="font-size: 80%;"><b>3D volumes of neurons</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs010.html#more-on-dimensionalities" style="font-size: 80%;"><b>More on Dimensionalities</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs011.html#further-remarks" style="font-size: 80%;"><b>Further remarks</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs012.html#layers-used-to-build-cnns" style="font-size: 80%;"><b>Layers used to build CNNs</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs013.html#transforming-images" style="font-size: 80%;"><b>Transforming images</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs014.html#cnns-in-brief" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs015.html#a-deep-cnn-model-from-raschka-et-al-https-github-com-rasbt-machine-learning-book" style="font-size: 80%;"><b>A deep CNN model ("From Raschka et al":"https://github.com/rasbt/machine-learning-book")</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs016.html#key-idea" style="font-size: 80%;"><b>Key Idea</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs017.html#how-to-do-image-compression-before-the-era-of-deep-learning" style="font-size: 80%;"><b>How to do image compression before the era of deep learning</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs018.html#the-svd-example" style="font-size: 80%;"><b>The SVD example</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs019.html#mathematics-of-cnns" style="font-size: 80%;"><b>Mathematics of CNNs</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs020.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;"><b>Convolution Examples: Polynomial multiplication</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs021.html#efficient-polynomial-multiplication" style="font-size: 80%;"><b>Efficient Polynomial Multiplication</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs022.html#further-simplification" style="font-size: 80%;"><b>Further simplification</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs023.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;"><b>A more efficient way of coding the above Convolution</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs024.html#commutative-process" style="font-size: 80%;"><b>Commutative process</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs025.html#toeplitz-matrices" style="font-size: 80%;"><b>Toeplitz matrices</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs026.html#fourier-series-and-toeplitz-matrices" style="font-size: 80%;"><b>Fourier series and Toeplitz matrices</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs027.html#generalizing-the-above-one-dimensional-case" style="font-size: 80%;"><b>Generalizing the above one-dimensional case</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs028.html#memory-considerations" style="font-size: 80%;"><b>Memory considerations</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs029.html#padding" style="font-size: 80%;"><b>Padding</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs030.html#new-vector" style="font-size: 80%;"><b>New vector</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs031.html#rewriting-as-dot-products" style="font-size: 80%;"><b>Rewriting as dot products</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#cross-correlation" style="font-size: 80%;"><b>Cross correlation</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs032.html#two-dimensional-objects" style="font-size: 80%;"><b>Two-dimensional objects</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs033.html#cnns-in-more-detail-simple-example" style="font-size: 80%;"><b>CNNs in more detail, simple example</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs034.html#the-convolution-stage" style="font-size: 80%;"><b>The convolution stage</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs035.html#finding-the-number-of-parameters" style="font-size: 80%;"><b>Finding the number of parameters</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs036.html#new-image-or-volume" style="font-size: 80%;"><b>New image (or volume)</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs037.html#parameters-to-train-common-settings" style="font-size: 80%;"><b>Parameters to train, common settings</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs038.html#examples-of-cnn-setups" style="font-size: 80%;"><b>Examples of CNN setups</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs039.html#summarizing-performing-a-general-discrete-convolution-from-raschka-et-al-https-github-com-rasbt-machine-learning-book" style="font-size: 80%;"><b>Summarizing: Performing a general discrete convolution ("From Raschka et al":"https://github.com/rasbt/machine-learning-book")</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs040.html#pooling" style="font-size: 80%;"><b>Pooling</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs041.html#pooling-arithmetic" style="font-size: 80%;"><b>Pooling arithmetic</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs042.html#pooling-types-from-raschka-et-al-https-github-com-rasbt-machine-learning-book" style="font-size: 80%;"><b>Pooling types ("From Raschka et al":"https://github.com/rasbt/machine-learning-book")</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs043.html#building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;"><b>Building convolutional neural networks in Tensorflow and Keras</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs044.html#setting-it-up" style="font-size: 80%;"><b>Setting it up</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs045.html#the-mnist-dataset-again" style="font-size: 80%;"><b>The MNIST dataset again</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs046.html#strong-correlations" style="font-size: 80%;"><b>Strong correlations</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs047.html#layers-of-a-cnn" style="font-size: 80%;"><b>Layers of a CNN</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs048.html#systematic-reduction" style="font-size: 80%;"><b>Systematic reduction</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs049.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;"><b>Prerequisites: Collect and pre-process data</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs050.html#importing-keras-and-tensorflow" style="font-size: 80%;"><b>Importing Keras and Tensorflow</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs051.html#running-with-keras" style="font-size: 80%;"><b>Running with Keras</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs052.html#final-part" style="font-size: 80%;"><b>Final part</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs053.html#final-visualization" style="font-size: 80%;"><b>Final visualization</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs054.html#the-cifar01-data-set" style="font-size: 80%;"><b>The CIFAR01 data set</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs055.html#verifying-the-data-set" style="font-size: 80%;"><b>Verifying the data set</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs056.html#set-up-the-model" style="font-size: 80%;"><b>Set up the model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs057.html#add-dense-layers-on-top" style="font-size: 80%;"><b>Add Dense layers on top</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs058.html#compile-and-train-the-model" style="font-size: 80%;"><b>Compile and train the model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs059.html#finally-evaluate-the-model" style="font-size: 80%;"><b>Finally, evaluate the model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#building-our-own-cnn-code" style="font-size: 80%;"><b>Building our own CNN code</b></a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#list-of-contents" style="font-size: 80%;"> List of contents:</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#schedulers" style="font-size: 80%;"> Schedulers</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#usage-of-schedulers" style="font-size: 80%;"> Usage of schedulers</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#cost-functions" style="font-size: 80%;"> Cost functions</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#usage-of-cost-functions" style="font-size: 80%;"> Usage of cost functions</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#activation-functions" style="font-size: 80%;"> Activation functions</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#usage-of-activation-functions" style="font-size: 80%;"> Usage of activation functions</a></li>
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<!-- navigation toc: --> <li><a href="._week44-bs060.html#convolution" style="font-size: 80%;"> Convolution</a></li>
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||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#layers" style="font-size: 80%;"> Layers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#convolution2dlayer-convolution-in-a-hidden-layer" style="font-size: 80%;"> Convolution2DLayer: convolution in a hidden layer</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#backpropagation-in-the-convolutional-layer" style="font-size: 80%;"> Backpropagation in the convolutional layer</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#demonstration" style="font-size: 80%;"> Demonstration</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#pooling-layer" style="font-size: 80%;"> Pooling Layer</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#flattening-layer" style="font-size: 80%;"> Flattening Layer</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#fully-connected-layers" style="font-size: 80%;"> Fully Connected Layers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#optimized-convolution2dlayer" style="font-size: 80%;"> Optimized Convolution2DLayer</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#the-convolutional-neural-network-cnn" style="font-size: 80%;"> The Convolutional Neural Network (CNN)</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#usage-of-cnn-code" style="font-size: 80%;"> Usage of CNN code</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#additional-remarks" style="font-size: 80%;"> Additional Remarks</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#remarks-on-the-speed" style="font-size: 80%;"> Remarks on the speed</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#convolution-using-separable-kernels" style="font-size: 80%;"> Convolution using separable kernels</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week44-bs060.html#convolution-in-the-fourier-domain" style="font-size: 80%;"> Convolution in the Fourier domain</a></li>
|
||
|
||
</ul>
|
||
</li>
|
||
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||
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0000"></a>
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<!-- ------------------- main content ---------------------- -->
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<center>
|
||
<h1>Week 44, Convolutional Neural Networks (CNN)</h1>
|
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</center> <!-- document title -->
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|
||
<!-- author(s): Morten Hjorth-Jensen -->
|
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<b>Morten Hjorth-Jensen</b>
|
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|
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<!-- institution -->
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||
<b>Department of Physics, University of Oslo, Norway</b>
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<br>
|
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<center>
|
||
<h4>October 28</h4>
|
||
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<br>
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<p><a href="._week44-bs001.html" class="btn btn-primary btn-lg">Read »</a></p>
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