A two layer perceptron implemented in MatLab to recogniz

# Recognizing Handwritten Digits using a Two-layer Perceptron This repository contains code corresponding to the seminar paper: D. Stutz. **Introduction to Neural Networks.** Seminar Report, Human Language Technology and Pattern Recognition Group, RWTH Aachen University, 2014. Advisor: Pavel Golik **Update:** The code can be adapted to allow mini-batch training as done in [this fork](https://github.com/Myasuka/matlab-mnist-two-layer-perceptron). ## MNIST Dataset The [MNIST dataset](http://yann.lecun.com/exdb/mnist/) provides a training set of 60,000 handwritten digits and a validation set of 10,000 handwritten digits. The images have size 28 x 28 pixels. Therefore, when using a two-layer perceptron, we need 28 x 28 = 784 input units and 10 output units (representing the 10 different digits). The methods `loadMNISTImages` and `loadMNISTLaels` are used to load the MNIST dataset as it is stored in a special file format. The methods can be found online at [http://ufldl.stanford.edu/wiki/index.php/Using_the_MNIST_Dataset](http://ufldl.stanford.edu/wiki/index.php/Using_the_MNIST_Dataset). ## Methods and Usage The main method to train the two-layer perceptron is `trainStochasticSquaredErrorTwoLayerPerceptron`. The method applies stochastic training (or to be precise a stochastic variant of mini-batch training) using the sum-of-squared error function and the error backpropagation algorithm. function [hiddenWeights, outputWeights, error] = trainStochasticSquaredErrorTwoLayerPerceptron(activationFunction, dActivationFunction, numberOfHiddenUnits, inputValues, targetValues, epochs, batchSize, learningRate) % trainStochasticSquaredErrorTwoLayerPerceptron Creates a two-layer perceptron % and trains it on the MNIST dataset. % % INPUT: % activationFunction : Activation function used in both layers. % dActivationFunction : Derivative of the activation % function used in both layers. % numberOfHiddenUnits : Number of hidden units. % inputValues : Input values for training (784 x 60000) % targetValues : Target values for training (1 x 60000) % epochs : Number of epochs to train. % batchSize : Plot error after batchSize images. % learningRate : Learning rate to apply. % % OUTPUT: % hiddenWeights : Weights of the hidden layer. % outputWeights : Weights of the output layer. % The above method requires the activation function used for both the hidden and the output layer to be given as parameter. I used the logistic sigmoid activation function: function y = logisticSigmoid(x) % simpleLogisticSigmoid Logistic sigmoid activation function % % INPUT: % x : Input vector. % % OUTPUT: % y : Output vector where the logistic sigmoid was applied element by % element. % In addition, the error backpropagation algorithm needs the derivative of the used activation function: function y = dLogisticSigmoid(x) % dLogisticSigmoid Derivative of the logistic sigmoid. % % INPUT: % x : Input vector. % % OUTPUT: % y : Output vector where the derivative of the logistic sigmoid was % applied element by element. % The method `applyStochasticSquaredErrorTwoLayerPerceptronMNIST` uses both the training method seen above and the method `validateTwoLayerPerceptron` to evaluate the performance of the two-layer perceptron: function [correctlyClassified, classificationErrors] = validateTwoLayerPerceptron(activationFunction, hiddenWeights, outputWeights, inputValues, labels) % validateTwoLayerPerceptron Validate the twolayer perceptron using the % validation set. % % INPUT: % activationFunction : Activation function used in both layers. % hiddenWeights : Weights of the hidden layer. % outputWeights : Weights of the output layer. % inputValues : Input values for training (784 x 10000). % labels : Labels for validation (1 x 10000). % % OUTPUT: % correctlyClassified : Number of correctly classified values. % classificationErrors : Number of classification errors. % ## License License for source code corresponding to: D. Stutz. **Introduction to Neural Networks.** Seminar Report, Human Language Technology and Pattern Recognition Group, RWTH Aachen University, 2014. Copyright (c) 2014-2018 David Stutz **Please read carefully the following terms and conditions and any accompanying documentation before you download and/or use this software and associated documentation files (the "Software").** The authors hereby grant you a non-exclusive, non-transferable, free of charge right to copy, modify, merge, publish, distribute, and sublicense the Software for the sole purpose of performing non-commercial scientific research, non-commercial education, or non-commercial artistic projects. Any other use, in particular any use for commercial purposes, is prohibited. This includes, without limitation, incorporation in a commercial product, use in a commercial service, or production of other artefacts for commercial purposes. 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