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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.

MNIST Dataset

The MNIST dataset 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.

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.

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").

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