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.

Copyright (c) 2014-2018 David Stutz

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