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(m,1) X];
yc = [];
for nex = 1:m
yc = [yc; zeros(1, y(nex)-1) 1 zeros(1, num_labels - y(nex))];
end
yc = yc';
a2 = sigmoid(Theta1 * X');
a2 = [ones(1, m); a2];
h = sigmoid(Theta2 * a2);
% un log likelihood
%J = mean(sum(-yc .* log(h) - (1 - yc) .* log(1 - h)));
% squared error
J = (1/(2*m)) * sum(sum((yc - h).^2));
% Regularisation
J = J + (lambda / (2 * m)) * ...
(sum(sum(Theta1(:,2:end).^2)) + sum(sum(Theta2(:,2:end).^2)));
Delta2 = zeros(size(Theta2));
Delta1 = zeros(size(Theta1));
for nex = 1:m
a1 = X(nex, :);
z2 = Theta1 * a1';
a2 = [1; sigmoid(z2)];
z3 = Theta2 * a2;
a3 = sigmoid(z3);
d3 = a3 - yc(:, nex);
Delta2 = Delta2 + d3 * a2';
d2 = Theta2' * d3;
d2 = d2(2:end) .* (sigmoid(z2).*(1 - sigmoid(z2)));
Delta1 = Delta1 + d2 * a1;
end
Theta2_grad = (1/m) * Delta2 + (lambda / m) * ...
[zeros(num_labels,1) Theta2(:,2:end)];
Theta1_grad = (1/m) * Delta1 + (lambda / m) * ...
[zeros(hidden_layer_size,1) Theta1(:,2:end)];
% -------------------------------------------------------------
% =========================================================================
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end