function [J grad] = nnCostFunction(nn_params, ...
input_layer_size, ...
hidden_layer_size, ...
num_labels, ...
X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
% [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
% X, y, lambda) computes the cost and gradient of the neural network. The
% parameters for the neural network are "unrolled" into the vector
% nn_params and need to be converted back into the weight matrices.
%
% The returned parameter grad should be a "unrolled" vector of the
% partial derivatives of the neural network.
%
% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
hidden_layer_size, (input_layer_size + 1));
Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
num_labels, (hidden_layer_size + 1));
% Setup some useful variables
m = size(X, 1);
% You need to return the following variables correctly
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));
% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
% following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
% variable J. After implementing Part 1, you can verify that your
% cost function computation is correct by verifying the cost
% computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
% Theta1_grad and Theta2_grad. You should return the partial derivatives of
% the cost function with respect to Theta1 and Theta2 in Theta1_grad and
% Theta2_grad, respectively. After implementing Part 2, you can check
% that your implementation is correct by running checkNNGradients
%
% Note: The vector y passed into the function is a vector of labels
% containing values from 1..K. You need to map this vector into a
% binary vector of 1's and 0's to be used with the neural network
% cost function.
%
% Hint: We recommend implementing backpropagation using a for-loop
% over the training examples if you are implementing it for the
% first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
% Hint: You can implement this around the code for
% backpropagation. That is, you can compute the gradients for
% the regularization separately and then add them to Theta1_grad
% and Theta2_grad from Part 2.
%
%
%X = [ones(size(X, 1), 1) X];
p = zeros(size(X, 1), 1);
h1 = sigmoid([ones(m, 1) X] * Theta1');
h2 = sigmoid([ones(m, 1) h1] * Theta2');
tempy = zeros(m, num_labels);
for k = 1:num_labels
tempy(:, k) = (y == k);
endfor
K = num_labels;
for i = 1:m
% iterativ
%for k = 1:K
% temp_y = (y == k);
% J += -temp_y(i) * log(h2(i,k)) - (1 - temp_y(i)) * log(1 - h2(i,k));
%endfor
%vectorizat
J += sum(-tempy(i, :) * log(h2(i, :)') - (1 - tempy(i, :)) * log(1 - h2(i, :)'));
endfor
J = J/m;
%vectorizat
J += lambda/(2*m) * (sum(sum(Theta1(:, 2:end) .* Theta1(:, 2:end)), 2) + sum(sum(Theta2(:, 2:end) .* Theta2(:, 2:end)), 2));
JCost = 0;
%for j = 1:25
% iterativ
%for k = 2:401
%JCost += Theta1(j,k)*Theta1(j,k);
%endfor
%vectorized
% JCost += sum(Theta1(j, 2:end) .* Theta1(j, 2:end));
%endfor
%for j = 1:10
%iterativ
%for k = 2:26
%JCost += Theta2(j,k)*Theta2(j,k);
%endfor
%vectorized
% JCost += sum(Theta2(j, 2:end) .* Theta2(j, 2:end));
%endfor
% -------------------------------------------------------------
Delta_1 = zeros(size(Theta1));
Delta_2 = zeros(size(Theta2));
for t = 1:m
% Pasul 1
a_1 = [1 ; X(t, :)'];
z_2 = Theta1 * a_1;
a_2 = [1 ; sigmoid(z_2)];
z_3 = Theta2 * a_2;
a_3 = sigmoid(z_3);
% Pasul 2
delta_3 = zeros(num_labels, 1);
for k = 1:num_labels
delta_3(k) = a_3(k) - (y == k)(t);
endfor
% Pasul 3
delta_2 = (Theta2)' * delta_3 .* sigmoidGradient([1; z_2]);
delta_2 = delta_2(2:end);
Delta_1 = Delta_1 + delta_2 * (a_1');
Delta_2 = Delta_2 + delta_3 * (a_2');
endfor
% =========================================================================
Theta1_grad(:, 1) = Delta_1(:, 1) ./ m;
Theta2_grad(:, 1) = Delta_2(:, 1) ./ m;
Theta1_grad(:, 2:end) = Delta_1(:, 2:end) ./ m + lambda/m .* Theta1(:, 2:end);
Theta2_grad(:, 2:end) = Delta_2(:, 2:end) ./ m + lambda/m .* Theta2(:, 2:end);
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end
