% This program illustrates how MultiClass works and trains the neural
%network max_epoch times. Once the training process has been finished, the program
%enters the training data into the neural network and displays the output. We
%can verify the training results via the comparison of the output with the correct
%output. See Chapter 4 for more information.

clear all
close all
clc

rng(3);

% The input set consists of five 5x5 pixel squares.
%0: white pixel; 1: black pixel.
X = zeros(5, 5, 7);   %(pixel_x, pixels_y, samples)
X(:, :, 1) = [0 1 1 0 0;
              0 0 1 0 0;
              0 0 1 0 0;
              0 0 1 0 0;
              0 1 1 1 0]; %1
          
X(:, :, 2) = [1 1 1 1 0;
              0 0 0 0 1;
              0 1 1 1 0;
              1 0 0 0 0;
              1 1 1 1 1]; %2
          
X(:, :, 3) = [1 1 1 1 0;
              0 0 0 0 1;
              0 1 1 1 0;
              0 0 0 0 1;
              1 1 1 1 0]; %3

X(:, :, 4) = [0 0 0 1 0;
              0 0 1 1 0;
              0 1 0 1 0;
              1 1 1 1 1;
              0 0 0 1 0]; %4
          
X(:, :, 5) = [1 1 1 1 1;
              1 0 0 0 0;
              1 1 1 1 0;
              0 0 0 0 1;
              1 1 1 1 0]; %5

X(:, :, 6) = [1 1 1 1 1;
              1 0 0 0 0;
              1 1 1 1 1;
              1 0 0 0 1;
              1 1 1 1 1]; %6
          
X(:, :, 7) = [1 1 1 1 1;
              0 0 0 0 1;
              0 0 0 1 0;
              0 0 0 1 0;
              0 0 0 1 0]; %7
% Desired outputs mapped via one-hot encoding (or 1-of-N encoding):
D = [1 0 0 0 0 0 0;     %1
     0 1 0 0 0 0 0;     %2
     0 0 1 0 0 0 0;     %3
     0 0 0 1 0 0 0;     %4
     0 0 0 0 1 0 0;     %5
     0 0 0 0 0 1 0;     %6
     0 0 0 0 0 0 1];    %7
% D = eye(7);

% Weights initialization:
W1 = 2*rand(50, 25) - 1; %(hidden neurons) x (inputs)
W2 = 2*rand( 7, 50) - 1; %(outputs) x (hidden neurons)

% Training process:
max_epoch = 10000;
for epoch = 1:max_epoch
    [W1, W2] = MultiClass(W1, W2, X, D);
end

% Inference:
N = size(X,3);
y = zeros(N,size(D,2));
for k = 1:N
    x = reshape(X(:, :, k), 25, 1);
    v1 = W1*x;
    y1 = Sigmoid(v1);
    v = W2*y1;
    y(k,:) = Softmax(v);
end

disp('Results:');
disp('   [desired]:');
disp(D);
disp('   [network_output]:');
disp(y)

%% Showing images (comment this section before running RealMultiClass.m):
% for i = 1:N
%     compareImages(X(:,:,i), y(i,:));
% end