function [W1, W2] = MultiClass(W1, W2, X, D)

% The function MultiClass.m implements the learning rule of multiclass
%classification using the SGD method and cross entropy cost function (see 
%Chapter 3 for more information about cross entropy function). 
%It takes the input arguments of the weights and training data and returns 
%the trained weights.

    alpha = 0.9;
    N = size(X,3); %number of samples
    
    for k = 1:N
        x = reshape(X(:, :, k), 25, 1);  %reorganizes the k-th sample into a 25x1 vector
        d = D(k, :)';   %desired output
        
        v1 = W1*x;
        y1 = Sigmoid(v1);
        v = W2*y1;
        y = Softmax(v);
        
        e = d - y;
        delta = e;
        
        e1 = W2'*delta;
        delta1 = y1.*(1-y1).*e1;
        dW1 = alpha*delta1*x';
        W1 = W1 + dW1;
        
        dW2 = alpha*delta*y1';
        W2 = W2 + dW2;
    end
end