1 function W = randInitializeWeights(L_in, L_out)
 2 %RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in
 3 %incoming connections and L_out outgoing connections
 4 %   W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights 
 5 %   of a layer with L_in incoming connections and L_out outgoing 
 6 %   connections. 
 7 %
 8 %   Note that W should be set to a matrix of size(L_out, 1 + L_in) as
 9 %   the column row of W handles the "bias" terms
10 %
11 % You need to return the following variables correctly 
12 W = zeros(L_out, 1 + L_in);
13 
14 % ====================== YOUR CODE HERE ======================
15 % Instructions: Initialize W randomly so that we break the symmetry while
16 %               training the neural network.
17 %
18 % Note: The first row of W corresponds to the parameters for the bias units
19 %
20 epsilon_init = 0.12;
21 W = rand(L_out, 1 + L_in) * 2 * epsilon_init - epsilon_init;
22 
23 % =========================================================================
24 
25 end

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));% Theta1_grad is a 25*401 matrix
Theta2_grad = zeros(size(Theta2));% Theta2_grad is a 10*26 matrix

% ====================== 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
X = [ones(m,1) X]; %5000*401
a_super2 = sigmoid(Theta1 * X‘); % attention a_super2 is a 25*5000 matrix
a_super2 = [ones(1,m);a_super2]; %add each bias unit for a_superscript2, 26 * 5000

% attention a_super3 is a 10 * 5000 matrix, each column is a predict value
a_super3 = sigmoid(Theta2 * a_super2);%10*5000

a3 = 1 - a_super3;%10*5000

%将5000条的结果label 向量y 转化成元素只为0或1 的矩阵Y
Y = zeros(num_labels, m); %10*5000, each column is a label result
for i = 1:num_labels
    Y(i, y==i)=1;
end

Y1 = 1 - Y;
res1 = 0;
res2 = 0;
for j = 1:m
    %两个矩阵的每一列相乘,再把结果求和。预测值和结果label对应的元素相乘,就是某个输入x 的代价
    tmp1 = sum( log(a_super3(:,j)) .* Y(:,j) ); 
    res1 = res1 + tmp1; % m 列之和
    tmp2 = sum( log(a3(:,j)) .* Y1(:,j) );
    res2 = res2 + tmp2;
end
J = (-res1 - res2) / 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.
%

for i = 1:m
    a1 = X(i, :)‘; %the i th input variables, 400*1
    z2 = Theta1 *  a1;
    a2 =  sigmoid( z2 ); % Theta1 * x superscript i
    a2 = [ 1; a2 ];% add bias unit, a2‘s size is 26 * 1
    z3 = Theta2 * a2;
    a3 = sigmoid( z3 ); % h_theta(x)
    
    error_3 = a3 - Y( :, i ); % last layer‘s error, 10*1
    %error_2 = ( Theta2‘ * error_3 ) .*  ( a2 .* (1 - a2) );% g‘(z2)=g(z2)*(1-g(z2)), 26*1
    
    err_2 =  Theta2‘ * error_3; % 26*1
    error_2 = ( err_2(2:end) ) .*  sigmoidGradient(z2);% 去掉 bias unit 对应的 error units
    
    Theta2_grad = Theta2_grad + error_3 * a2‘;
    Theta1_grad = Theta1_grad + error_2 * a1‘;
end

Theta2_grad = Theta2_grad / m; % video 9-2 backpropagation algorithm the 11 th minute
Theta1_grad = Theta1_grad / m;

% 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.
%

% reg for cost function J,  ex4.pdf page 6 
Theta1_tmp = Theta1(:, 2:end).^2;
Theta2_tmp = Theta2(:, 2:end).^2;
reg = lambda / (2*m) * ( sum( Theta1_tmp(:) ) + sum( Theta2_tmp(:) ) );

J = (-res1 - res2) / m + reg;
% -------------------------------------------------------------

% reg for bp, ex4.pdf materials page 11
Theta1(:,1) = 0;
Theta2(:,1) = 0;

Theta1_grad = Theta1_grad + lambda / m * Theta1;
Theta2_grad = Theta2_grad + lambda / m * Theta2;
% =========================================================================

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