Machine learning 第5周编程作业

1.Sigmoid Gradient

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

　　

2.nnCostFunction

这是一道综合问题；

Ⅰ：计算代价函数J（前向传播）

Ⅱ：BackPropagation

Ⅲ：正则化；

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.
%

X=[ones(m,1) X];
a1=Theta1*X';
z1=[ones(m,1),sigmoid(a1)'];
a2=Theta2*z1';
h=sigmoid(a2);

yy=zeros(m,num_labels);
for i=1:m,
  yy(i,y(i))=1;
endfor
J=1/m*sum( sum( (-yy).*log(h')-(1-yy).*log(1-h') ) );

J=J+lambda/(2*m)*( sum(sum(Theta1(:,2:end).^2))+sum(sum(Theta2(:,2:end).^2)));

for i=1:m,
  a1=X(i,:)';
  z2=Theta1*a1;
  a2=[1;sigmoid(z2)];
  z3=Theta2*a2;
  a3=sigmoid(z3);
  tmpy=yy(i,:);
  dlt3=a3-tmpy';
  dlt2=(Theta2(:,2:end)'*dlt3.*sigmoidGradient(z2));

  Theta1_grad=Theta1_grad+dlt2*a1';
  Theta2_grad=Theta2_grad+dlt3*a2';
endfor

Theta1_grad=Theta1_grad./m;
Theta2_grad=Theta2_grad./m;

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