ex4.m

%% Neural Network Learning with Backpropagation

%% Initialization
clear ; close all; clc

%% Setup the parameters you will use for this exercise
inputLayerSize  = 400;  % 20x20 Input Images of Digits
hiddenLayerSize = 25;   % 25 hidden units
numberOfLabels = 10;    % 10 labels, from 1 to 10   
                        % (note that we have mapped "0" to label 10)

%% =========== Part 1: Loading and Visualizing Data =============
%  We start the exercise by first loading and visualizing the dataset. 
%  You will be working with a dataset that contains handwritten digits.

% Load Training Data
fprintf('Loading and Visualizing Data ...\n')

load('ex4data1.mat');
m = size(X, 1);

% Randomly select 100 data points to display
sel = randperm(size(X, 1));
sel = sel(1:100);

displayData(X(sel, :));
title('Example of 100 Randomly Selected Digits from Input Training Set');

fprintf('Program paused. Press enter to continue.\n');
pause;


%% ================ Part 2: Loading Parameters ================
% In this part of the exercise, we load some pre-initialized 
% neural network parameters.

fprintf('\nLoading Saved Neural Network Parameters ...\n')

% Load the weights into variables Theta1 and Theta2
load('ex4weights.mat');

% Unroll parameters by converting the matrix into a single long column vector
neuralNetworkParameters = [Theta1(:) ; Theta2(:)];

%% ================ Part 3: Compute Cost (Feedforward) ================
%  To the neural network, you should first start by implementing the
%  feedforward part of the neural network that returns the cost only. You
%  should complete the code in nnCostFunction.m to return cost. After
%  implementing the feedforward to compute the cost, you can verify that
%  your implementation is correct by verifying that you get the same cost
%  as us for the fixed debugging parameters.
%
%  We suggest implementing the feedforward cost *without* regularization
%  first so that it will be easier for you to debug. Later, in part 4, you
%  will get to implement the regularized cost.
%
fprintf('\nFeedforward Using Neural Network ...\n')

% Weight regularization parameter (we set this to 0 here).
lambda = 0;

J = nnCostFunction(neuralNetworkParameters, inputLayerSize, hiddenLayerSize, ...
                   numberOfLabels, X, y, lambda);

fprintf(['Cost at parameters (loaded from ex4weights): %f '...
         '\n(this value should be about 0.287629)\n'], J);

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% =============== Part 4: Implement Regularization ===============
%  Once your cost function implementation is correct, you should now
%  continue to implement the regularization with the cost.
%

fprintf('\nChecking Cost Function (w/ Regularization) ... \n')

% Weight regularization parameter (we set this to 1 here).
lambda = 1;

J = nnCostFunction(neuralNetworkParameters, inputLayerSize, hiddenLayerSize, ...
                   numberOfLabels, X, y, lambda);

fprintf(['Cost at parameters (loaded from ex4weights): %f '...
         '\n(this value should be about 0.383770)\n'], J);

fprintf('Program paused. Press enter to continue.\n');
pause;


%% ================ Part 5: Sigmoid Gradient  ================
%  Before you start implementing the neural network, you will first
%  implement the gradient for the sigmoid function. You should complete the
%  code in the sigmoidGradient.m file.
%

fprintf('\nEvaluating sigmoid gradient...\n')

g = sigmoidGradient([1 -0.5 0 0.5 1]);
fprintf('Sigmoid gradient evaluated at [1 -0.5 0 0.5 1]:\n  ');
fprintf('%f ', g);
fprintf('\n\n');

fprintf('Program paused. Press enter to continue.\n');
pause;


%% ================ Part 6: Initializing Pameters ================
%  In this part of the exercise, you will be starting to implment a two
%  layer neural network that classifies digits. You will start by
%  implementing a function to initialize the weights of the neural network
%  (randInitializeWeights.m)

fprintf('\nInitializing Neural Network Parameters ...\n')

initial_Theta1 = randInitializeWeights(inputLayerSize, hiddenLayerSize);
initial_Theta2 = randInitializeWeights(hiddenLayerSize, numberOfLabels);

% Unroll parameters
initial_nn_params = [initial_Theta1(:) ; initial_Theta2(:)];


%% =============== Part 7: Implement Backpropagation ===============
%  Once your cost matches up with ours, you should proceed to implement the
%  backpropagation algorithm for the neural network. You should add to the
%  code you've written in nnCostFunction.m to return the partial
%  derivatives of the parameters.
%
fprintf('\nChecking Backpropagation... \n');

%  Check gradients by running checkNNGradients
checkNNGradients;

fprintf('\nProgram paused. Press enter to continue.\n');
pause;


%% =============== Part 8: Implement Regularization ===============
%  Once your backpropagation implementation is correct, you should now
%  continue to implement the regularization with the cost and gradient.
%

fprintf('\nChecking Backpropagation (w/ Regularization) ... \n')

%  Check gradients by running checkNNGradients
lambda = 3;
checkNNGradients(lambda);

% Also output the costFunction debugging values
debug_J  = nnCostFunction(neuralNetworkParameters, inputLayerSize, ...
                          hiddenLayerSize, numberOfLabels, X, y, lambda);

fprintf(['\n\nCost at (fixed) debugging parameters (w/ lambda = 10): %f ' ...
         '\n(this value should be about 0.576051)\n\n'], debug_J);

fprintf('Program paused. Press enter to continue.\n');
pause;


%% =================== Part 8: Training NN ===================
%  You have now implemented all the code necessary to train a neural 
%  network. To train your neural network, we will now use "fmincg", which
%  is a function which works similarly to "fminunc". Recall that these
%  advanced optimizers are able to train our cost functions efficiently as
%  long as we provide them with the gradient computations.
%
fprintf('\nTraining Neural Network... \n')

%  After you have completed the assignment, change the MaxIter to a larger
%  value to see how more training helps.
options = optimset('MaxIter', 50);

%  You should also try different values of lambda
lambda = 1;

% Create "short hand" for the cost function to be minimized
costFunction = @(p) nnCostFunction(p, ...
                                   inputLayerSize, ...
                                   hiddenLayerSize, ...
                                   numberOfLabels, X, y, lambda);

% Now, costFunction is a function that takes in only one argument (the
% neural network parameters)
[neuralNetworkParameters, cost] = fmincg(costFunction, initial_nn_params, options);

% Obtain Theta1 and Theta2 back from neuralNetworkParameters
Theta1 = reshape(neuralNetworkParameters(1:hiddenLayerSize * (inputLayerSize + 1)), ...
                 hiddenLayerSize, (inputLayerSize + 1));

Theta2 = reshape(neuralNetworkParameters((1 + (hiddenLayerSize * (inputLayerSize + 1))):end), ...
                 numberOfLabels, (hiddenLayerSize + 1));

fprintf('Program paused. Press enter to continue.\n');
pause;


%% ================= Part 9: Visualize Weights =================
%  You can now "visualize" what the neural network is learning by 
%  displaying the hidden units to see what features they are capturing in 
%  the data.

fprintf('\nVisualizing Neural Network... \n')

displayData(Theta1(:, 2:end));

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ================= Part 10: Implement Predict =================
%  After training the neural network, we would like to use it to predict
%  the labels. You will now implement the "predict" function to use the
%  neural network to predict the labels of the training set. This lets
%  you compute the training set accuracy.

pred = predict(Theta1, Theta2, X);

fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);