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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.
%
%% calculate J
% recode y
Y = diag(ones(1, num_labels));
X = [ones(m, 1) X]; % 5000 * 401
aa2 = sigmoid(Theta1 * X'); % 25 * 5000
aa22 = [ones(1, m); aa2];
aa3 = sigmoid(Theta2 * aa22); % 10 * 5000
for
i = 1: m
tempJ = -Y(:, y(i)) .* log(aa3(:, i)) - (1 - Y(:, y(i))) .* log(1 - aa3(:, i));
sum_tempJ = sum(tempJ);
J = J + sum_tempJ;
end
J = 1/m * J;
% regular
temp_theta1 = Theta1(:, (2: end));
temp_theta2 = Theta2(:, (2: end));
J = J + lambda * 1/(2*m) * (sum(sum(temp_theta1.^2)) + sum(sum(temp_theta2.^2)));
%% Calculate grad
Delta1 = 0;
Delta2 = 0;
Delta3 = 0;
for
i = 1: m
a1 = X(i, :)'; % 401*1
z2 = Theta1 * a1; % 25*1
a2_temp = sigmoid(z2);
a2 = [1; a2_temp]; % 26*1
z3 = Theta2 * a2; % 10*1
a3_temp = sigmoid(z3);
% a3 = [1; a3_temp];
delta3 = a3_temp - Y(:, y(i)); *1
delta2 = Theta2(:, [2:end])' * delta3 .* sigmoidGradient(z2); % 25*1
Delta2 = Delta2 + delta3 * a2'; % 10*26
Delta1 = Delta1 + delta2 * a1'; % 25*401
end
Theta1_grad = 1/m * Delta1;
Theta2_grad = 1/m * Delta2;
%% Regularized
[m1, n1] = size(Theta1);
[m2, n2] = size(Theta2);
Theta1_grad = Theta1_grad + lambda / m * [zeros(m1, 1), Theta1(:, [2: end])];
Theta2_grad = Theta2_grad + lambda / m * [zeros(m2, 1), Theta2(:, [2: end])];
% -------------------------------------------------------------
% =========================================================================
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end
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