吳恩達的機器學習程式設計作業11:nnCostFunction 求解神經網路的代價函式(含BP演算法)
阿新 • • 發佈:2019-02-04
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. % Y=zeros(size(y,1),num_labels); for i=1:size(y,1) Y(i,y(i,1)) = 1; end a1 = [ones(size(X,1),1) X]; a2=sigmoid(a1*Theta1'); a2 = [ones(size(a1,1),1) a2]; h=sigmoid(a2*Theta2'); J=(1/m)*sum(sum((-Y).*log(h) -(1.-Y).*log(1.-h))); r = (lambda / (2 * m)) * (sum(sum(Theta1(:, 2:end) .^ 2)) + sum(sum(Theta2(:, 2:end) .^ 2))); J = J+r; for i = 1:m a1 = [1 X(i,:)]'; z2 = Theta1 * a1; a2 = sigmoid(z2); a2 = [1; a2]; z3=Theta2 * a2; a3 = sigmoid(z3); d3 = a3 - Y'(:, i); d2 = (Theta2' * d3) .*a2.*(1.-a2); d2 = d2(2:end); Theta1_grad = Theta1_grad + d2 * a1'; Theta2_grad = Theta2_grad + d3 * a2'; end Theta1_grad = Theta1_grad ./ m; Theta1_grad(:, 2:end) = Theta1_grad(:, 2:end) + (lambda/m) * Theta1(:, 2:end); Theta2_grad = Theta2_grad ./ m; Theta2_grad(:, 2:end) = Theta2_grad(:, 2:end)+ (lambda/m) * Theta2(:, 2:end); % ------------------------------------------------------------- % ========================================================================= % Unroll gradients grad = [Theta1_grad(:) ; Theta2_grad(:)]; end