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147 lines
5.3 KiB
Matlab
147 lines
5.3 KiB
Matlab
function [J grad] = nnCostFunction(nn_params, ...
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input_layer_size, ...
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hidden_layer_size, ...
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num_labels, ...
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X, y, lambda)
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%NNCOSTFUNCTION Implements the neural network cost function for a two layer
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%neural network which performs classification
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% [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
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% X, y, lambda) computes the cost and gradient of the neural network. The
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% parameters for the neural network are "unrolled" into the vector
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% nn_params and need to be converted back into the weight matrices.
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%
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% The returned parameter grad should be a "unrolled" vector of the
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% partial derivatives of the neural network.
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%
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% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
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% for our 2 layer neural network
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Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
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hidden_layer_size, (input_layer_size + 1));
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Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
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num_labels, (hidden_layer_size + 1));
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% Setup some useful variables
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m = size(X, 1);
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% You need to return the following variables correctly
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J = 0;
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Theta1_grad = zeros(size(Theta1));
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Theta2_grad = zeros(size(Theta2));
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% ====================== YOUR CODE HERE ======================
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% Instructions: You should complete the code by working through the
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% following parts.
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%
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% Part 1: Feedforward the neural network and return the cost in the
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% variable J. After implementing Part 1, you can verify that your
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% cost function computation is correct by verifying the cost
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% computed in ex4.m
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%
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X = [ones(m, 1), X]; % add a first colum of ones (bias term)
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A_2 = sigmoid(X*Theta1');
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A_2 = [ones(m, 1), A_2]; % (bias term)
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A_3 = sigmoid(A_2*Theta2');
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h_0 = A_3;
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%disp(round(h_0));
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% y is 1x5000 and holds the labels as numbers, turn it into 5000x10,
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% each row holding the label as vectors, e.g. [0 1 0 0 0 ... ] for 2.
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y = eye(num_labels)(y,:); % y is used as an index, it gets a row,
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% e.g. [0 0 0 1 ... 0 0]
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assert(size(y) == [m num_labels]);
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J = 1/m * sum(sum(-y.*log(h_0) - (1-y).*log(1-h_0)));
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assert(size(J) == [1 1]);
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% Part 2: Implement the backpropagation algorithm to compute the gradients
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% Theta1_grad and Theta2_grad. You should return the partial derivatives of
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% the cost function with respect to Theta1 and Theta2 in Theta1_grad and
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% Theta2_grad, respectively. After implementing Part 2, you can check
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% that your implementation is correct by running checkNNGradients
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%
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% Note: The vector y passed into the function is a vector of labels
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% containing values from 1..K. You need to map this vector into a
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% binary vector of 1's and 0's to be used with the neural network
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% cost function.
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%
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% Hint: We recommend implementing backpropagation using a for-loop
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% over the training examples if you are implementing it for the
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% first time.
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%
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D_1 = zeros(size(Theta1));
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D_2 = zeros(size(Theta2));
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for t = 1:m
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% feed forward this training sample
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% ---------------------------------------------------------------------------
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a_1 = X(t,:);
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% (X already has 1-column)
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assert(size(a_1) == [1, input_layer_size+1]);
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z_2 = a_1*Theta1';
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a_2 = sigmoid(z_2);
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a_2 = [ones(size(a_2, 1)), a_2]; % (bias term)
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assert(size(a_2) == [1, hidden_layer_size+1]);
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z_3 = a_2*Theta2';
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a_3 = sigmoid(z_3);
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h_0 = a_3;
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assert(size(h_0) == [1, num_labels]);
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% back propagate / error
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% ---------------------------------------------------------------------------
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assert(size(y) == [m num_labels]);
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d_3 = a_3 - y(t,:);
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assert(size(d_3) == [1, num_labels]);
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d_2 = d_3*Theta2 .* [1, sigmoidGradient(z_2)];
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d_2 = d_2(2:end);
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assert(size(d_2) == [1, hidden_layer_size]);
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% accumulate over all m training examples
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D_2 = D_2 + d_3'*a_2;
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D_1 = D_1 + d_2'*a_1;
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end
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% average
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D_2 /= m;
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D_1 /= m;
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Theta2_grad = D_2;
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Theta1_grad = D_1;
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% Part 3: Implement regularization with the cost function and gradients.
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%
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% Hint: You can implement this around the code for
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% backpropagation. That is, you can compute the gradients for
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% the regularization separately and then add them to Theta1_grad
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% and Theta2_grad from Part 2.
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%
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% Note: Theta1/2 are matrixes here, we want all their rows, but skip their
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% first column (not regularizing the bias term).
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J_regularization_term = lambda/(2*m) * ...
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(sum(sum(Theta1(:,2:end).^2)) ...
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+ sum(sum(Theta2(:,2:end).^2)));
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assert(size(J_regularization_term) == [1 1]);
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J += J_regularization_term;
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Theta2_grad_regularization_term = lambda/m * [zeros(size(Theta2, 1), 1) Theta2(:,2:end)];
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Theta1_grad_regularization_term = lambda/m * [zeros(size(Theta1, 1), 1) Theta1(:,2:end)];
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Theta2_grad += Theta2_grad_regularization_term;
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Theta1_grad += Theta1_grad_regularization_term;
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% -------------------------------------------------------------
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% =========================================================================
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% Unroll gradients
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grad = [Theta1_grad(:) ; Theta2_grad(:)];
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end
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