Coursera-机器学习-吴恩达-ex4

代码和作业说明下载
这次作业我们需要实现 Neural Networks Learning。

需要完成下列代码文件：

• sigmoidGradient.m
• randInitializeWeights.m
• nnCostFunction.m

sigmoidGradient.m

matlab

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

matlab

function W = randInitializeWeights(L_in, L_out)
%RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in
%incoming connections and L_out outgoing connections
%   W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights 
%   of a layer with L_in incoming connections and L_out outgoing 
%   connections. 
%
%   Note that W should be set to a matrix of size(L_out, 1 + L_in) as
%   the first column of W handles the "bias" terms
%

% You need to return the following variables correctly 
W = zeros(L_out, 1 + L_in);

% ====================== YOUR CODE HERE ======================
% Instructions: Initialize W randomly so that we break the symmetry while
%               training the neural network.
%
% Note: The first column of W corresponds to the parameters for the bias unit
%

epsilon_init  = 0.12;
W = rand(L_out, 1 + L_in) * 2 * epsilon_init - epsilon_init;








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

end

nnCostFunction.m

matlab

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];

Y_tmp = zeros(m, num_labels);

for i = 1 : m
  Y_tmp(i, y(i)) = 1;
end

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

J = (-1 / m) * sum(sum((Y_tmp .* log(h) + (1 - Y_tmp) .* log(1 - h))'));
%--------------------------------------------------------------------------

Theta1_tmp = Theta1(:, 2:end);
Theta2_tmp = Theta2(:, 2:end);
regular_term = (lambda / (2 * m)) * (sum(sum((Theta1_tmp .^ 2)')) + ...
                  sum(sum((Theta2_tmp .^ 2)')));
J = J + regular_term;

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

Yk = zeros(m, num_labels);

for i = 1 : m
  Yk(i, y(i)) = 1;
end

%{

for i = 1 : m
  a1 = [1, X(i, :)];  % 1x401
  z2 = a1 * Theta1';
  a2 = sigmoid(z2);
  a2 = [1, a2];       % 1x26
  z3 = a2 * Theta2';
  a3 = sigmoid(z3);
  delta3 = a3 - Yk(i, :); % 1x10
  delta2 = delta3 * Theta2(:, 2:end) .* sigmoidGradient(z2); % 1x25
  
  Theta1_grad = Theta1_grad + delta2' * a1;
  Theta2_grad = Theta2_grad + delta3' * a2;
  
endfor

%}

a1 = [ones(m, 1) X];  % 5000 x 401
z2 = a1 * Theta1';    % 5000 x 401  401 x 25 -> 5000 x 25
a2 = [ones(m, 1) sigmoid(z2)];     % 5000 x 26
z3 = a2 * Theta2';    % 5000 x 26   26 x 10  -> 5000 - 10
a3 = sigmoid(z3);     % 5000 x 10
delta3 = a3 - Yk;     % 5000 x 10
delta2 = delta3 * Theta2(:, 2:end) .* sigmoidGradient(z2); % 5000 x 10  10 x 25 -> 5000 x 25

Theta1_grad = Theta1_grad + delta2' * a1;           % 25 x 5000  5000 x 401   -> 25 x 401
Theta2_grad = Theta2_grad + delta3' * a2;           % 10 x 5000  5000 x 26    -> 10 x 26



Theta1_grad = Theta1_grad ./ m;
Theta2_grad = Theta2_grad ./ m;
%----------------------------------------------------------------
Theta1_tmp = Theta1;
Theta2_tmp = Theta2;
Theta1_tmp(:, 1) = 0;
Theta2_tmp(:, 1) = 0;

Theta1_grad = Theta1_grad + (lambda / m) .* Theta1_tmp;

Theta2_grad = Theta2_grad + (lambda / m) .* Theta2_tmp;


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

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


end