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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. %
ylable = eye(num_labels)(y,:);
a1 = [ones(m,1) X]; z2 = a1 * Theta1'; a2 = sigmoid(z2); a2 = [ones(m,1) a2]; a3 = sigmoid(a2 * Theta2');
% 这里不知道为什么用向量的形式写出来是不对的? %J = 1 / m * (-ylable' * log(a3) - (1 - ylable') * log(1 - a3)); J = 1 / m * sum( sum( -ylable.* log(a3) - (1-ylable).*log(1-a3) ));
% pay attention :" Theta1(:,2:end) " , no "Theta1" . regularized = lambda/(2*m) * (sum(sum(Theta1(:,2:end).^2)) + sum(sum(Theta2(:,2:end).^2)) ); J = J + regularized;
delta3 = a3-ylable; %5000x10 delta2 = delta3 * Theta2 ; delta2 = delta2(:,2:end); delta2 = delta2 .* sigmoidGradient(z2); %5000x25 Delta_1 = zeros(size(Theta1)); Delta_2 = zeros(size(Theta2)); Delta_1 = Delta_1 + delta2' * a1 ; Delta_2 = Delta_2 + delta3' * a2 ; Theta1_grad = 1/m * Delta_1; Theta2_grad = 1/m * Delta_2; regularized_1 = lambda/m * Theta1; regularized_2 = lambda/m * Theta2; % j = 0是不需要正则化的 regularized_1(:,1) = zeros(size(regularized_1,1),1); regularized_2(:,1) = zeros(size(regularized_2,1),1); Theta1_grad = Theta1_grad + regularized_1; Theta2_grad = Theta2_grad + regularized_2;
% =========================================================================
% Unroll gradients grad = [Theta1_grad(:) ; Theta2_grad(:)];
end
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