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Matlab

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
%
X = [ones(m, 1), X]; % add a first colum of ones (bias term)
A_2 = sigmoid(X*Theta1');
A_2 = [ones(m, 1), A_2]; % (bias term)
A_3 = sigmoid(A_2*Theta2');
h_0 = A_3;
%disp(round(h_0));
% y is 1x5000 and holds the labels as numbers, turn it into 5000x10,
% each row holding the label as vectors, e.g. [0 1 0 0 0 ... ] for 2.
y = eye(num_labels)(y,:); % y is used as an index, it gets a row,
% e.g. [0 0 0 1 ... 0 0]
assert(size(y) == [m num_labels]);
J = 1/m * sum(sum(-y.*log(h_0) - (1-y).*log(1-h_0)));
assert(size(J) == [1 1]);
% 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.
%
D_1 = zeros(size(Theta1));
D_2 = zeros(size(Theta2));
for t = 1:m
% feed forward this training sample
% ---------------------------------------------------------------------------
a_1 = X(t,:);
% (X already has 1-column)
assert(size(a_1) == [1, input_layer_size+1]);
z_2 = a_1*Theta1';
a_2 = sigmoid(z_2);
a_2 = [ones(size(a_2, 1)), a_2]; % (bias term)
assert(size(a_2) == [1, hidden_layer_size+1]);
z_3 = a_2*Theta2';
a_3 = sigmoid(z_3);
h_0 = a_3;
assert(size(h_0) == [1, num_labels]);
% back propagate / error
% ---------------------------------------------------------------------------
assert(size(y) == [m num_labels]);
d_3 = a_3 - y(t,:);
assert(size(d_3) == [1, num_labels]);
d_2 = d_3*Theta2 .* [1, sigmoidGradient(z_2)];
d_2 = d_2(2:end);
assert(size(d_2) == [1, hidden_layer_size]);
% accumulate over all m training examples
D_2 = D_2 + d_3'*a_2;
D_1 = D_1 + d_2'*a_1;
end
% average
D_2 /= m;
D_1 /= m;
Theta2_grad = D_2;
Theta1_grad = D_1;
% 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.
%
% Note: Theta1/2 are matrixes here, we want all their rows, but skip their
% first column (not regularizing the bias term).
regularization_term = lambda/(2*m) * ...
(sum(sum(Theta1(:,2:end).^2)) ...
+ sum(sum(Theta2(:,2:end).^2)));
assert(size(regularization_term) == [1 1]);
J += regularization_term;
% -------------------------------------------------------------
% =========================================================================
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end