《机器学习》学习笔记（二）：神经网络

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. % J_tmp=zeros(m,1); for i=1:m y_vec=zeros(num_labels,1); y_vec(y(i))=1; a1 = [ones(1, 1) X(i,:)]'; z2=Theta1*a1; a2=sigmoid(z2); a2=[ones(1,size(a2,2)); a2]; z3=Theta2*a2; a3=sigmoid(z3); hThetaX=a3; J_tmp(i)=sum(-y_vec.*log(hThetaX)-(1-y_vec).*log(1-hThetaX)); end J=1/m*sum(J_tmp); J=J+lambda/(2*m)*(sum(sum(Theta1(:,2:end).^2))+sum(sum(Theta2(:,2:end).^2))); Delta1 = zeros( hidden_layer_size, (input_layer_size + 1)); Delta2 = zeros( num_labels, (hidden_layer_size + 1)); for t=1:m y_vec=zeros(num_labels,1); y_vec(y(t))=1; a1 = [1 X(t,:)]'; z2=Theta1*a1; a2=sigmoid(z2); a2=[ones(1,size(a2,2)); a2]; z3=Theta2*a2; a3=sigmoid(z3); delta_3=a3-y_vec; gz2=[0;sigmoidGradient(z2)]; delta_2=Theta2'*delta_3.*gz2; delta_2=delta_2(2:end); Delta2=Delta2+delta_3*a2'; Delta1=Delta1+delta_2*a1'; end Theta1_grad=1/m*Delta1; Theta2_grad=1/m*Delta2; Theta1(:,1)=0; Theta1_grad=Theta1_grad+lambda/m*Theta1; Theta2(:,1)=0; Theta2_grad=Theta2_grad+lambda/m*Theta2; % ------------------------------------------------------------- % ========================================================================= % Unroll gradients grad = [Theta1_grad(:) ; Theta2_grad(:)]; end