machine-learning第五周 上机作业

毫无疑问，难度越来越大了，首先我们得复习相关概念：

1、导数（变化率）与微分 （变化量）

2、数学里的 e 为什么叫做自然底数？

3、女神的文章必不可少

剩下的必须慢慢啃了。总之，本章要完全理解我觉得不太可能，但必须能明白nnCostFunction里的每一步。

代码如下：

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.%% part 1% Theta1 has size 25 x 401% Theta2 has size 10 x 26y = eye(num_labels)(y,:); %5000x10a1 = [ones(m, 1) X];      %5000x401z2 = a1 * Theta1' ;a2 = sigmoid(z2);         n = size(a2,1);a2 = [ones(n, 1) a2] ;    %5000x26a3 = sigmoid(a2 * Theta2'); %5000x10J = sum( sum( -y.* log(a3) -  (1-y).*log(1-a3) ))/ m;% 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;  % part 2delta3 = a3-y;            %5000x10delta2 = delta3 * Theta2 ;delta2 = delta2(:,2:end);   delta2 = delta2 .* sigmoidGradient(z2);  %5000x25Delta_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;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;%Theta1_grad = ((1/m) * Delta_1) + ((lambda/m) * (Theta1));%Theta2_grad = ((1/m) * Delta_2) + ((lambda/m) * (Theta2));%Theta1_grad(:,1) -= ((lambda/m) * (Theta1(:,1)));%Theta2_grad(:,1) -= ((lambda/m) * (Theta2(:,1)));% -------------------------------------------------------------% =========================================================================% Unroll gradientsgrad = [Theta1_grad(:) ; Theta2_grad(:)];end