Programming Exercise 4: Neural Networks Learning Machine Learning

大家好，今天总结Coursera网课上Andrew Ng MachineLearning 第四次作业
(1) nnCostFunction.m

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.
%

a1= [ones(m, 1) X];
z2=Theta1*a1';
a2=sigmoid(z2);
a2=[ones(1,m);a2];
z3=Theta2*a2;
a3=sigmoid(z3);
h=a3;
%把label形式的y转换为向量形式的y；
y_vect=zeros(num_labels,m);
for i=1:m
    y_vect(y(i),i)=1;
end
for i=1:m
    J=J+1/m*sum(-log(h(:,i))'*y_vect(:,i)-log(1-h(:,i))'*(1-y_vect(:,i)));
end

%costFunction结束
%正则化
Theta1_use=Theta1(:,2:end);
Theta2_use=Theta2(:,2:end);
J=J+lambda/(2*m)*(sum(sum(Theta1_use.^2))+sum(sum(Theta2_use.^2)));
%计算梯度
%Δ的元素个数应该和对应的theta中的元素的个数相同
Delta1 = zeros(size(Theta1));
Delta2 = zeros(size(Theta2));
for i=1:m
    delta3=a3(:,i)-y_vect(:,i);
    %注意这里的δ是不包含bias unit的delta的，毕竟bias unit永远是1，
    %不需要计算delta, 下面的2:end,: 过滤掉了bias unit相关值
    temp=Theta2'*delta3;
    delta2=temp(2:end,:).*sigmoidGradient(z2(:,i));
    Delta2=Delta2+delta3*a2(:,i)';
    Delta1=Delta1+delta2*a1(i,:);
    % -------------------------------------------------------------
end
Theta1_grad=Delta1/m;
Theta2_grad=Delta2/m;
Theta1_grad(:,2:end)=Theta1_grad(:,2:end)+lambda/m*Theta1(:,2:end);
Theta2_grad(:,2:end)=Theta2_grad(:,2:end)+lambda/m*Theta2(:,2:end);
% =========================================================================

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

end

(2)sigmoidGradient.m

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