Coursera Machine Learning 第五周 quiz Programming Exercise 4: Neural Networks Learning

nnCostFunction.m

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 networkTheta1 = 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 variablesm = 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.% %计算J值X = [ones(m,1) X];for i = 1:m,                                                               %m为训练样本数，利用for遍历    z2 = Theta1 * X(i,:)';                                                 %对第i个训练样本正向传播得到输出h(x)，即为a3    a2 = sigmoid(z2);    a2 = [1; a2];    z3 = Theta2 * a2;    a3 = sigmoid(z3);    J = J + sum(log(1 - a3)) + log(a3(y(i,:))) - log(1 - a3(y(i,:)));      %由于输出为10维向量，而y的值是1-10的数字，所以可以用y的值指示a3那些元素加，哪些不加end                                                                        %a3(y(i，：))及指示训练样本对应的a3的元素J = -1/m * J;temp = 0;for i = 1:hidden_layer_size,                                               %对Theta1除了第一列（与偏置神经元对应的那列）元素的平方求和                                            for j = 2:(input_layer_size + 1),        temp = temp + Theta1(i,j)^2;    endendfor i = 1:num_labels,                                                       %对Theta2除了第一列（与偏置神经元对应的那列）元素的平方求和     for j = 2:(hidden_layer_size + 1),        temp = temp + Theta2(i,j)^2;    endendJ = J + lambda/(2*m)*temp;%利用反向传播法求取偏导数值，实际上这个循环可以和计算J值得循环合为一个，为了代码清晰，所以分开写了delta3 = zeros(num_labels,1);                                              %反向传播，输出层的误差delta2  = zeros(size(Theta1));                                             %反向传播，隐藏层的误差；输入层不计算误差for i = 1:m,                                                               %m为训练样本数，利用for遍历    a1 = X(i,:)';    z2 = Theta1 * a1;                                                      %对第i个训练样本正向传播得到输出h(x)，即为a3    a2 = sigmoid(z2);    a2 = [1; a2];    z3 = Theta2 * a2;    a3 = sigmoid(z3);    delta3 = a3;                                                           %反向传播，计算得偏导数    delta3(y(i,:)) = delta3(y(i,:)) - 1;    delta2 = Theta2' * delta3 .*[1;sigmoidGradient(z2)];    delta2 = delta2(2:end);    Theta2_grad = Theta2_grad + delta3 * a2';    Theta1_grad = Theta1_grad + delta2 * a1';end Theta2_grad = 1/m * Theta2_grad + lambda/m * Theta2;                       %正则化，修正梯度值Theta2_grad(:,1) = Theta2_grad(:,1) - lambda/m * Theta2(:,1);              %由于不惩罚偏执单元对应的列，所以把他减掉Theta1_grad = 1/m * Theta1_grad + lambda/m * Theta1;                       %同理修改Theta1_gradTheta1_grad(:,1) = Theta1_grad(:,1) - lambda/m * Theta1(:,1);% -------------------------------------------------------------% =========================================================================% Unroll gradientsgrad = [Theta1_grad(:) ; Theta2_grad(:)];end

sigmoidGradient.m

function g = sigmoidGradient(z)%SIGMOIDGRADIENT returns the gradient of the sigmoid function%evaluated at z%   g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function%   evaluated at z. This should work regardless if z is a matrix or a%   vector. In particular, if z is a vector or matrix, you should return%   the gradient for each element.g = zeros(size(z));% ====================== YOUR CODE HERE ======================% Instructions: Compute the gradient of the sigmoid function evaluated at%               each value of z (z can be a matrix, vector or scalar).g = sigmoid(z).*(1-sigmoid(z));  % =============================================================end