ex4-1 : neural networks

• 1. feedforward and cost function (without regularization)
• 2. regularized cost function

1. feedforward and cost function (without regularization)

nnCostFunction.m

function [J grad] = nnCostFunction(nn_params, ...  
                                   input_layer_size, ...  
                                   hidden_layer_size, ...  
                                   num_labels, ...  
                                   X, y, lambda)  

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));  

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

% Calculate h(x) through the forward propagation   
X = [ones(m, 1) X];        % X: 5000x(400+1)  
a2 = sigmoid(X * Theta1');    % theta1: 25x401  

a2 = [ones(m, 1) a2];        % a2: 5000x(25+1)  
a3 = sigmoid(a2 * Theta2');    % theta2: 10x26  
                % a3: 5000x10  
                % h(x) == a3   
                % a3의 하나의 row에서 1열 ~ 10(K)열은 각각이 class를 나타냄. 1 ~ 10까지  
                % 따라서 Y(5000x10) 의 각 열은 1부터 10으로 채워져야함 -> 아님.  
% Generate Y: 오답  
%Y = zeros(m, num_labels);  
%for i=1:m  
%    for j=1:num_labels  
%        Y(:,j) = j;  
%    end  
%end  

% Generate Y: 정답  
% 하나의 row는 하나의 y 벡터여야함. 결과값 y(10x1) 벡터는 하나만 1이고 나머지는 0임.  
% Y는 y'한것을 m(row갯수) 만큼 이어붙임 '  
I = eye(num_labels);  
Y = zeros(m, num_labels);  
for i=1:m  
    Y(i, :)= I(y(i), :);  
end  

% Cost function J1  

pos = -Y .* log(a3);        % Y: 5000x10, a3: 5000x10  
                % Y .* a3: 5000x10  
neg = (1 - Y) .* log(1 - a3);  

J = (1/m) * sum(sum(pos - neg,2),1);

2. regularized cost function

% Cost function J + regularization  
% theta1: 25x401  
% theta2: 10x26  

Theta1Reg = Theta1(:,2:size(Theta1,2));  
Theta2Reg = Theta2(:,2:size(Theta2,2));  

Reg = sum(sum((Theta1Reg).^2, 2)) + sum(sum((Theta2Reg).^2, 2));  
J = J + (lambda/(2*m))*Reg;