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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.
%
A1 = [ones(m, 1) X];
Z2 = A1 * Theta1';
A2 = [ones(m, 1) sigmoid(Z2)];
Z3 = A2 * Theta2';
A3 = sigmoid(Z3);
Y = zeros(size(A3));
for i = 1 : m
Y(i, y(i, 1)) = 1;
end
J = J + 1/m * sum(sum(-Y .* log(A3) - (1 - Y) .* log(1 - A3)));
J = J + lambda/(2 * m) * sum(sum(Theta1(:, 2 : end) .^ 2));
J = J + lambda/(2 * m) * sum(sum(Theta2(:, 2 : end) .^ 2));
Delta3 = A3 - Y;
Delta2 = (Delta3 * Theta2);
Delta2 = Delta2(:, 2:end) .* sigmoidGradient(Z2);
Theta1_grad = Theta1_grad + 1/m * (Delta2' * A1);
Theta2_grad = Theta2_grad + 1/m * (Delta3' * A2);
Theta1_temp = Theta1;
Theta1_temp(:, 1) = 0;
Theta1_grad = Theta1_grad + lambda/m * Theta1_temp;
Theta2_temp = Theta2;
Theta2_temp(:, 1) = 0;
Theta2_grad = Theta2_grad + lambda/m * Theta2_temp;
% -------------------------------------------------------------
% =========================================================================
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
endfunction