吴恩达机器学习编程作业与笔记（4）第5周：Neural Networks: Learning神经网络：学习

sigmoidGradient.m - Compute the gradient of the sigmoid function

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

randInitializeWeights.m - Randomly initialize weights

好像这个文件并不需要进行什么操作

nnCostFunction.m - Neural network cost function

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.
%
% part1
% 计算假设函数
a1 = [ones(m,1) X];
z2 = a1 * Theta1';
a2 = sigmoid(z2);
a2 = [ones(size(a2,1),1) a2];
z3 = a2 * Theta2';
a3 = sigmoid(z3);
h = a3;     % 5000 x 10


% y是m x 1向量,需要变成m x 10矩阵
u = eye(num_labels);

% 这条语句有点难理解，大概意思是选出每一行的y值作为u的行标，将这行u替换对应行的y
y = u(y,:);         

J = 1/m * sum(sum(-y .* log(h) - (1 - y) .* log(1 - h)));

% 对X添加一列
X = [ones(m,1) X];
% 正则化 （向量化形式）
regularization = lambda / (2*m) * (sum(sum(Theta1(:, 2:end).^2))+ sum(sum(Theta2(: , 2:end).^2 )));
J += regularization;
% part2
delta3 = a3 - y;           % 5000 x 10
delta2 = delta3 * Theta2;  % 5000 x 26
delta2 = delta2(:,2:end);  % 5000 x 25
delta2 = delta2 .* sigmoidGradient(z2);    % 5000 x 25

Delta1 = zeros(size(Theta1));
Delta2 = zeros(size(Theta2));

Delta1 = Delta1 + delta2' * a1;    % 26 x 400
Delta2 = Delta2 + delta3' * a2;    % 10 x 25

Theta1_grad = 1 / m * Delta1 + lambda / m * Theta1 ;
Theta2_grad = 1 / m * Delta2 + lambda /m  * Theta2 ;

% 0号元素不用正则化
Theta1_grad(:,1) -=  lambda / m * Theta1(:,1); 
Theta2_grad(:,1) -=  lambda / m * Theta2(:,1);



















% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end