Morten Hjorth-Jensen
577 lines
46 KiB
HTML
577 lines
46 KiB
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'sections': [('Plan for week 41', 2, None, 'plan-for-week-41'),
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('Videos on Neural Networks',
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2,
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None,
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'videos-on-neural-networks'),
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('Setting up the Back propagation algorithm',
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None,
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('Setting up a Multi-layer perceptron model for classification',
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None,
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('Defining the cost function',
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('Example: binary classification problem',
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('The Softmax function', 2, None, 'the-softmax-function'),
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('Developing a code for doing neural networks with back '
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('Collect and pre-process data',
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('Define model and architecture',
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('Weights and biases', 2, None, 'weights-and-biases'),
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('Feed-forward pass', 2, None, 'feed-forward-pass'),
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('Matrix multiplications', 2, None, 'matrix-multiplications'),
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('Choose cost function and optimizer',
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2,
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None,
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'choose-cost-function-and-optimizer'),
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('Optimizing the cost function',
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'optimizing-the-cost-function'),
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('Regularization', 2, None, 'regularization'),
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('Matrix multiplication', 2, None, 'matrix-multiplication'),
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('Improving performance', 2, None, 'improving-performance'),
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('Full object-oriented implementation',
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('Evaluate model performance on test data',
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('Adjust hyperparameters', 2, None, 'adjust-hyperparameters'),
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('Visualization', 2, None, 'visualization'),
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('scikit-learn implementation',
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'scikit-learn-implementation'),
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('Visualization', 2, None, 'visualization'),
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('Testing our code for the XOR, OR and AND gates',
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'testing-our-code-for-the-xor-or-and-and-gates'),
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('The AND and XOR Gates', 2, None, 'the-and-and-xor-gates'),
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('Representing the Data Sets',
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2,
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'representing-the-data-sets'),
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('Setting up the Neural Network',
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('The Code using Scikit-Learn',
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('Building neural networks in Tensorflow and Keras',
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('Tensorflow', 2, None, 'tensorflow'),
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('Using Keras', 2, None, 'using-keras'),
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('Collect and pre-process data',
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2,
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None,
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'collect-and-pre-process-data'),
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('The Breast Cancer Data, now with Keras',
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2,
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None,
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'the-breast-cancer-data-now-with-keras'),
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('The Mathematics of Neural Networks',
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2,
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None,
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'the-mathematics-of-neural-networks'),
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('Fine-tuning neural network hyperparameters',
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'fine-tuning-neural-network-hyperparameters'),
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('Hidden layers', 2, None, 'hidden-layers'),
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('Which activation function should I use?',
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2,
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None,
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'which-activation-function-should-i-use'),
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('Is the Logistic activation function (Sigmoid) our choice?',
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None,
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'is-the-logistic-activation-function-sigmoid-our-choice'),
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('The derivative of the Logistic funtion',
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2,
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None,
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'the-derivative-of-the-logistic-funtion'),
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('The RELU function family', 2, None, 'the-relu-function-family'),
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('Which activation function should we use?',
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2,
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None,
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'which-activation-function-should-we-use'),
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('More on activation functions, output layers',
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('Batch Normalization', 2, None, 'batch-normalization'),
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('Dropout', 2, None, 'dropout'),
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('Gradient Clipping', 2, None, 'gradient-clipping'),
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('A very nice website on Neural Networks',
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('A top-down perspective on Neural networks',
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('Limitations of supervised learning with deep networks',
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('Overarching Views, a personal note',
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'overarching-views-a-personal-note'),
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('From a Spherical Cow to a real one',
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('Convolutional Neural Networks (recognizing images)',
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('Regular NNs don’t scale well to full images',
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'regular-nns-don-t-scale-well-to-full-images'),
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('3D volumes of neurons', 2, None, '3d-volumes-of-neurons'),
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('Layers used to build CNNs',
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('Transforming images', 2, None, 'transforming-images'),
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('CNNs in brief', 2, None, 'cnns-in-brief'),
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('CNNs in more detail, building convolutional neural networks in '
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'cnns-in-more-detail-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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('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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('Fun links', 2, None, 'fun-links')]}
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<a class="navbar-brand" href="week41-bs.html">Week 41 Constructing a Neural Network code, Tensor flow and start Convolutional Neural Networks</a>
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<ul class="nav navbar-nav navbar-right">
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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="._week41-bs001.html#plan-for-week-41" style="font-size: 80%;">Plan for week 41</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs002.html#videos-on-neural-networks" style="font-size: 80%;">Videos on Neural Networks</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs003.html#setting-up-the-back-propagation-algorithm" style="font-size: 80%;">Setting up the Back propagation algorithm</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs004.html#setting-up-a-multi-layer-perceptron-model-for-classification" style="font-size: 80%;">Setting up a Multi-layer perceptron model for classification</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs005.html#defining-the-cost-function" style="font-size: 80%;">Defining the cost function</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs006.html#example-binary-classification-problem" style="font-size: 80%;">Example: binary classification problem</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs007.html#the-softmax-function" style="font-size: 80%;">The Softmax function</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs008.html#developing-a-code-for-doing-neural-networks-with-back-propagation" style="font-size: 80%;">Developing a code for doing neural networks with back propagation</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs035.html#collect-and-pre-process-data" style="font-size: 80%;">Collect and pre-process data</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs010.html#train-and-test-datasets" style="font-size: 80%;">Train and test datasets</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs011.html#define-model-and-architecture" style="font-size: 80%;">Define model and architecture</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs012.html#layers" style="font-size: 80%;">Layers</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs013.html#weights-and-biases" style="font-size: 80%;">Weights and biases</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs014.html#feed-forward-pass" style="font-size: 80%;">Feed-forward pass</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs015.html#matrix-multiplications" style="font-size: 80%;">Matrix multiplications</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs016.html#choose-cost-function-and-optimizer" style="font-size: 80%;">Choose cost function and optimizer</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs017.html#optimizing-the-cost-function" style="font-size: 80%;">Optimizing the cost function</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs018.html#regularization" style="font-size: 80%;">Regularization</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs019.html#matrix-multiplication" style="font-size: 80%;">Matrix multiplication</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs020.html#improving-performance" style="font-size: 80%;">Improving performance</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs021.html#full-object-oriented-implementation" style="font-size: 80%;">Full object-oriented implementation</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs022.html#evaluate-model-performance-on-test-data" style="font-size: 80%;">Evaluate model performance on test data</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs023.html#adjust-hyperparameters" style="font-size: 80%;">Adjust hyperparameters</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs026.html#visualization" style="font-size: 80%;">Visualization</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs025.html#scikit-learn-implementation" style="font-size: 80%;">scikit-learn implementation</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs026.html#visualization" style="font-size: 80%;">Visualization</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs027.html#testing-our-code-for-the-xor-or-and-and-gates" style="font-size: 80%;">Testing our code for the XOR, OR and AND gates</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs028.html#the-and-and-xor-gates" style="font-size: 80%;">The AND and XOR Gates</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs029.html#representing-the-data-sets" style="font-size: 80%;">Representing the Data Sets</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs030.html#setting-up-the-neural-network" style="font-size: 80%;">Setting up the Neural Network</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs031.html#the-code-using-scikit-learn" style="font-size: 80%;">The Code using Scikit-Learn</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs032.html#building-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">Building neural networks in Tensorflow and Keras</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs033.html#tensorflow" style="font-size: 80%;">Tensorflow</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs034.html#using-keras" style="font-size: 80%;">Using Keras</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs035.html#collect-and-pre-process-data" style="font-size: 80%;">Collect and pre-process data</a></li>
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<!-- navigation toc: --> <li><a href="#the-breast-cancer-data-now-with-keras" style="font-size: 80%;">The Breast Cancer Data, now with Keras</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs037.html#the-mathematics-of-neural-networks" style="font-size: 80%;">The Mathematics of Neural Networks</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs038.html#fine-tuning-neural-network-hyperparameters" style="font-size: 80%;">Fine-tuning neural network hyperparameters</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs039.html#hidden-layers" style="font-size: 80%;">Hidden layers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs040.html#which-activation-function-should-i-use" style="font-size: 80%;">Which activation function should I use?</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs041.html#is-the-logistic-activation-function-sigmoid-our-choice" style="font-size: 80%;">Is the Logistic activation function (Sigmoid) our choice?</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs042.html#the-derivative-of-the-logistic-funtion" style="font-size: 80%;">The derivative of the Logistic funtion</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs043.html#the-relu-function-family" style="font-size: 80%;">The RELU function family</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs044.html#which-activation-function-should-we-use" style="font-size: 80%;">Which activation function should we use?</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs045.html#more-on-activation-functions-output-layers" style="font-size: 80%;">More on activation functions, output layers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs046.html#batch-normalization" style="font-size: 80%;">Batch Normalization</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs047.html#dropout" style="font-size: 80%;">Dropout</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs048.html#gradient-clipping" style="font-size: 80%;">Gradient Clipping</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs049.html#a-very-nice-website-on-neural-networks" style="font-size: 80%;">A very nice website on Neural Networks</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs050.html#a-top-down-perspective-on-neural-networks" style="font-size: 80%;">A top-down perspective on Neural networks</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs051.html#limitations-of-supervised-learning-with-deep-networks" style="font-size: 80%;">Limitations of supervised learning with deep networks</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs052.html#overarching-views-a-personal-note" style="font-size: 80%;">Overarching Views, a personal note</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs053.html#from-a-spherical-cow-to-a-real-one" style="font-size: 80%;">From a Spherical Cow to a real one</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs054.html#convolutional-neural-networks-recognizing-images" style="font-size: 80%;">Convolutional Neural Networks (recognizing images)</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs055.html#regular-nns-don-t-scale-well-to-full-images" style="font-size: 80%;">Regular NNs don’t scale well to full images</a></li>
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||
<!-- navigation toc: --> <li><a href="._week41-bs056.html#3d-volumes-of-neurons" style="font-size: 80%;">3D volumes of neurons</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs057.html#layers-used-to-build-cnns" style="font-size: 80%;">Layers used to build CNNs</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs058.html#transforming-images" style="font-size: 80%;">Transforming images</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs059.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs060.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="._week41-bs061.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs062.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs063.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs064.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs065.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs066.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs067.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs068.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs069.html#final-part" style="font-size: 80%;">Final part</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs070.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week41-bs071.html#fun-links" style="font-size: 80%;">Fun links</a></li>
|
||
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
</div>
|
||
</div>
|
||
</div> <!-- end of navigation bar -->
|
||
|
||
<div class="container">
|
||
|
||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||
|
||
<a name="part0036"></a>
|
||
<!-- !split -->
|
||
|
||
<h2 id="the-breast-cancer-data-now-with-keras" class="anchor">The Breast Cancer Data, now with Keras </h2>
|
||
|
||
<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">tensorflow</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">tf</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> 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: #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">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
|
||
<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: #008000; font-weight: bold">as</span> splitter
|
||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
|
||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pickle</span>
|
||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">os</span>
|
||
|
||
|
||
<span style="color: #BA2121; font-style: italic">"""Load breast cancer dataset"""</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">#create same seed for random number every time</span>
|
||
|
||
cancer<span style="color: #666666">=</span>load_breast_cancer() <span style="color: #408080; font-style: italic">#Download breast cancer dataset</span>
|
||
|
||
inputs<span style="color: #666666">=</span>cancer<span style="color: #666666">.</span>data <span style="color: #408080; font-style: italic">#Feature matrix of 569 rows (samples) and 30 columns (parameters)</span>
|
||
outputs<span style="color: #666666">=</span>cancer<span style="color: #666666">.</span>target <span style="color: #408080; font-style: italic">#Label array of 569 rows (0 for benign and 1 for malignant)</span>
|
||
labels<span style="color: #666666">=</span>cancer<span style="color: #666666">.</span>feature_names[<span style="color: #666666">0</span>:<span style="color: #666666">30</span>]
|
||
|
||
<span style="color: #008000">print</span>(<span style="color: #BA2121">'The content of the breast cancer dataset is:'</span>) <span style="color: #408080; font-style: italic">#Print information about the datasets</span>
|
||
<span style="color: #008000">print</span>(labels)
|
||
<span style="color: #008000">print</span>(<span style="color: #BA2121">'-------------------------'</span>)
|
||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"inputs = "</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">"outputs = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(outputs<span style="color: #666666">.</span>shape))
|
||
<span style="color: #008000">print</span>(<span style="color: #BA2121">"labels = "</span><span style="color: #666666">+</span> <span style="color: #008000">str</span>(labels<span style="color: #666666">.</span>shape))
|
||
|
||
x<span style="color: #666666">=</span>inputs <span style="color: #408080; font-style: italic">#Reassign the Feature and Label matrices to other variables</span>
|
||
y<span style="color: #666666">=</span>outputs
|
||
|
||
<span style="color: #408080; font-style: italic">#%% </span>
|
||
|
||
<span style="color: #408080; font-style: italic"># Visualisation of dataset (for correlation analysis)</span>
|
||
|
||
plt<span style="color: #666666">.</span>figure()
|
||
plt<span style="color: #666666">.</span>scatter(x[:,<span style="color: #666666">0</span>],x[:,<span style="color: #666666">2</span>],s<span style="color: #666666">=40</span>,c<span style="color: #666666">=</span>y,cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>Spectral)
|
||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'Mean radius'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'Mean perimeter'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>show()
|
||
|
||
plt<span style="color: #666666">.</span>figure()
|
||
plt<span style="color: #666666">.</span>scatter(x[:,<span style="color: #666666">5</span>],x[:,<span style="color: #666666">6</span>],s<span style="color: #666666">=40</span>,c<span style="color: #666666">=</span>y, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>Spectral)
|
||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'Mean compactness'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'Mean concavity'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>show()
|
||
|
||
|
||
plt<span style="color: #666666">.</span>figure()
|
||
plt<span style="color: #666666">.</span>scatter(x[:,<span style="color: #666666">0</span>],x[:,<span style="color: #666666">1</span>],s<span style="color: #666666">=40</span>,c<span style="color: #666666">=</span>y,cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>Spectral)
|
||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'Mean radius'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'Mean texture'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>show()
|
||
|
||
plt<span style="color: #666666">.</span>figure()
|
||
plt<span style="color: #666666">.</span>scatter(x[:,<span style="color: #666666">2</span>],x[:,<span style="color: #666666">1</span>],s<span style="color: #666666">=40</span>,c<span style="color: #666666">=</span>y,cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>Spectral)
|
||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'Mean perimeter'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'Mean compactness'</span>,fontweight<span style="color: #666666">=</span><span style="color: #BA2121">'bold'</span>)
|
||
plt<span style="color: #666666">.</span>show()
|
||
|
||
|
||
<span style="color: #408080; font-style: italic"># Generate training and testing datasets</span>
|
||
|
||
<span style="color: #408080; font-style: italic">#Select features relevant to classification (texture,perimeter,compactness and symmetery) </span>
|
||
<span style="color: #408080; font-style: italic">#and add to input matrix</span>
|
||
|
||
temp1<span style="color: #666666">=</span>np<span style="color: #666666">.</span>reshape(x[:,<span style="color: #666666">1</span>],(<span style="color: #008000">len</span>(x[:,<span style="color: #666666">1</span>]),<span style="color: #666666">1</span>))
|
||
temp2<span style="color: #666666">=</span>np<span style="color: #666666">.</span>reshape(x[:,<span style="color: #666666">2</span>],(<span style="color: #008000">len</span>(x[:,<span style="color: #666666">2</span>]),<span style="color: #666666">1</span>))
|
||
X<span style="color: #666666">=</span>np<span style="color: #666666">.</span>hstack((temp1,temp2))
|
||
temp<span style="color: #666666">=</span>np<span style="color: #666666">.</span>reshape(x[:,<span style="color: #666666">5</span>],(<span style="color: #008000">len</span>(x[:,<span style="color: #666666">5</span>]),<span style="color: #666666">1</span>))
|
||
X<span style="color: #666666">=</span>np<span style="color: #666666">.</span>hstack((X,temp))
|
||
temp<span style="color: #666666">=</span>np<span style="color: #666666">.</span>reshape(x[:,<span style="color: #666666">8</span>],(<span style="color: #008000">len</span>(x[:,<span style="color: #666666">8</span>]),<span style="color: #666666">1</span>))
|
||
X<span style="color: #666666">=</span>np<span style="color: #666666">.</span>hstack((X,temp))
|
||
|
||
X_train,X_test,y_train,y_test<span style="color: #666666">=</span>splitter(X,y,test_size<span style="color: #666666">=0.1</span>) <span style="color: #408080; font-style: italic">#Split datasets into training and testing</span>
|
||
|
||
y_train<span style="color: #666666">=</span>to_categorical(y_train) <span style="color: #408080; font-style: italic">#Convert labels to categorical when using categorical cross entropy</span>
|
||
y_test<span style="color: #666666">=</span>to_categorical(y_test)
|
||
|
||
<span style="color: #008000; font-weight: bold">del</span> temp1,temp2,temp
|
||
|
||
<span style="color: #408080; font-style: italic"># %%</span>
|
||
|
||
<span style="color: #408080; font-style: italic"># Define tunable parameters"</span>
|
||
|
||
eta<span style="color: #666666">=</span>np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-3</span>,<span style="color: #666666">-1</span>,<span style="color: #666666">3</span>) <span style="color: #408080; font-style: italic">#Define vector of learning rates (parameter to SGD optimiser)</span>
|
||
lamda<span style="color: #666666">=0.01</span> <span style="color: #408080; font-style: italic">#Define hyperparameter</span>
|
||
n_layers<span style="color: #666666">=2</span> <span style="color: #408080; font-style: italic">#Define number of hidden layers in the model</span>
|
||
n_neuron<span style="color: #666666">=</span>np<span style="color: #666666">.</span>logspace(<span style="color: #666666">0</span>,<span style="color: #666666">3</span>,<span style="color: #666666">4</span>,dtype<span style="color: #666666">=</span><span style="color: #008000">int</span>) <span style="color: #408080; font-style: italic">#Define number of neurons per layer</span>
|
||
epochs<span style="color: #666666">=100</span> <span style="color: #408080; font-style: italic">#Number of reiterations over the input data</span>
|
||
batch_size<span style="color: #666666">=100</span> <span style="color: #408080; font-style: italic">#Number of samples per gradient update</span>
|
||
|
||
<span style="color: #408080; font-style: italic"># %%</span>
|
||
|
||
<span style="color: #BA2121; font-style: italic">"""Define function to return Deep Neural Network model"""</span>
|
||
|
||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">NN_model</span>(inputsize,n_layers,n_neuron,eta,lamda):
|
||
model<span style="color: #666666">=</span>Sequential()
|
||
<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>(n_layers): <span style="color: #408080; font-style: italic">#Run loop to add hidden layers to the model</span>
|
||
<span style="color: #008000; font-weight: bold">if</span> (i<span style="color: #666666">==0</span>): <span style="color: #408080; font-style: italic">#First layer requires input dimensions</span>
|
||
model<span style="color: #666666">.</span>add(Dense(n_neuron,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(lamda),input_dim<span style="color: #666666">=</span>inputsize))
|
||
<span style="color: #008000; font-weight: bold">else</span>: <span style="color: #408080; font-style: italic">#Subsequent layers are capable of automatic shape inferencing</span>
|
||
model<span style="color: #666666">.</span>add(Dense(n_neuron,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(lamda)))
|
||
model<span style="color: #666666">.</span>add(Dense(<span style="color: #666666">2</span>,activation<span style="color: #666666">=</span><span style="color: #BA2121">'softmax'</span>)) <span style="color: #408080; font-style: italic">#2 outputs - ordered and disordered (softmax for prob)</span>
|
||
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
|
||
|
||
|
||
Train_accuracy<span style="color: #666666">=</span>np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(n_neuron),<span style="color: #008000">len</span>(eta))) <span style="color: #408080; font-style: italic">#Define matrices to store accuracy scores as a function</span>
|
||
Test_accuracy<span style="color: #666666">=</span>np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(n_neuron),<span style="color: #008000">len</span>(eta))) <span style="color: #408080; font-style: italic">#of learning rate and number of hidden neurons for </span>
|
||
|
||
<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: #008000">len</span>(n_neuron)): <span style="color: #408080; font-style: italic">#run loops over hidden neurons and learning rates to calculate </span>
|
||
<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(eta)): <span style="color: #408080; font-style: italic">#accuracy scores </span>
|
||
DNN_model<span style="color: #666666">=</span>NN_model(X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">1</span>],n_layers,n_neuron[i],eta[j],lamda)
|
||
DNN_model<span style="color: #666666">.</span>fit(X_train,y_train,epochs<span style="color: #666666">=</span>epochs,batch_size<span style="color: #666666">=</span>batch_size,verbose<span style="color: #666666">=1</span>)
|
||
Train_accuracy[i,j]<span style="color: #666666">=</span>DNN_model<span style="color: #666666">.</span>evaluate(X_train,y_train)[<span style="color: #666666">1</span>]
|
||
Test_accuracy[i,j]<span style="color: #666666">=</span>DNN_model<span style="color: #666666">.</span>evaluate(X_test,y_test)[<span style="color: #666666">1</span>]
|
||
|
||
|
||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">plot_data</span>(x,y,data,title<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">None</span>):
|
||
|
||
<span style="color: #408080; font-style: italic"># plot results</span>
|
||
fontsize<span style="color: #666666">=16</span>
|
||
|
||
|
||
fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure()
|
||
ax <span style="color: #666666">=</span> fig<span style="color: #666666">.</span>add_subplot(<span style="color: #666666">111</span>)
|
||
cax <span style="color: #666666">=</span> ax<span style="color: #666666">.</span>matshow(data, interpolation<span style="color: #666666">=</span><span style="color: #BA2121">'nearest'</span>, vmin<span style="color: #666666">=0</span>, vmax<span style="color: #666666">=1</span>)
|
||
|
||
cbar<span style="color: #666666">=</span>fig<span style="color: #666666">.</span>colorbar(cax)
|
||
cbar<span style="color: #666666">.</span>ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">'accuracy (%)'</span>,rotation<span style="color: #666666">=90</span>,fontsize<span style="color: #666666">=</span>fontsize)
|
||
cbar<span style="color: #666666">.</span>set_ticks([<span style="color: #666666">0</span>,<span style="color: #666666">.2</span>,<span style="color: #666666">.4</span>,<span style="color: #666666">0.6</span>,<span style="color: #666666">0.8</span>,<span style="color: #666666">1.0</span>])
|
||
cbar<span style="color: #666666">.</span>set_ticklabels([<span style="color: #BA2121">'0%'</span>,<span style="color: #BA2121">'20%'</span>,<span style="color: #BA2121">'40%'</span>,<span style="color: #BA2121">'60%'</span>,<span style="color: #BA2121">'80%'</span>,<span style="color: #BA2121">'100%'</span>])
|
||
|
||
<span style="color: #408080; font-style: italic"># put text on matrix elements</span>
|
||
<span style="color: #008000; font-weight: bold">for</span> i, x_val <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(np<span style="color: #666666">.</span>arange(<span style="color: #008000">len</span>(x))):
|
||
<span style="color: #008000; font-weight: bold">for</span> j, y_val <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(np<span style="color: #666666">.</span>arange(<span style="color: #008000">len</span>(y))):
|
||
c <span style="color: #666666">=</span> <span style="color: #BA2121">"$</span><span style="color: #BB6688; font-weight: bold">{0:.1f}</span><span style="color: #BB6622; font-weight: bold">\\</span><span style="color: #BA2121">%$"</span><span style="color: #666666">.</span>format( <span style="color: #666666">100*</span>data[j,i])
|
||
ax<span style="color: #666666">.</span>text(x_val, y_val, c, va<span style="color: #666666">=</span><span style="color: #BA2121">'center'</span>, ha<span style="color: #666666">=</span><span style="color: #BA2121">'center'</span>)
|
||
|
||
<span style="color: #408080; font-style: italic"># convert axis vaues to to string labels</span>
|
||
x<span style="color: #666666">=</span>[<span style="color: #008000">str</span>(i) <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> x]
|
||
y<span style="color: #666666">=</span>[<span style="color: #008000">str</span>(i) <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> y]
|
||
|
||
|
||
ax<span style="color: #666666">.</span>set_xticklabels([<span style="color: #BA2121">''</span>]<span style="color: #666666">+</span>x)
|
||
ax<span style="color: #666666">.</span>set_yticklabels([<span style="color: #BA2121">''</span>]<span style="color: #666666">+</span>y)
|
||
|
||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">'$</span><span style="color: #BB6622; font-weight: bold">\\</span><span style="color: #BA2121">mathrm{learning</span><span style="color: #BB6622; font-weight: bold">\\</span><span style="color: #BA2121"> rate}$'</span>,fontsize<span style="color: #666666">=</span>fontsize)
|
||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">'$</span><span style="color: #BB6622; font-weight: bold">\\</span><span style="color: #BA2121">mathrm{hidden</span><span style="color: #BB6622; font-weight: bold">\\</span><span style="color: #BA2121"> neurons}$'</span>,fontsize<span style="color: #666666">=</span>fontsize)
|
||
<span style="color: #008000; font-weight: bold">if</span> title <span style="color: #AA22FF; font-weight: bold">is</span> <span style="color: #AA22FF; font-weight: bold">not</span> <span style="color: #008000; font-weight: bold">None</span>:
|
||
ax<span style="color: #666666">.</span>set_title(title)
|
||
|
||
plt<span style="color: #666666">.</span>tight_layout()
|
||
|
||
plt<span style="color: #666666">.</span>show()
|
||
|
||
plot_data(eta,n_neuron,Train_accuracy, <span style="color: #BA2121">'training'</span>)
|
||
plot_data(eta,n_neuron,Test_accuracy, <span style="color: #BA2121">'testing'</span>)
|
||
</pre></div>
|
||
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