Coursera—machine learning(Andrew Ng)第五周编程作业

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)) %g'(z)

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

end
randInitializeWeights.m



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


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
4000
* (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.
%
% part 1

% Theta1 has size 25 x 401
% Theta2 has size 10 x 26

h = eye(num_labels);
y = h(y,:); %5000x10 这两条语句的意义在将y中的值变为0-1表示
a1 = [ones(m, 1) X]; %5000x401
z2 = a1 * Theta1' ;
a2 = sigmoid(z2);
n = size(a2,1);
a2 = [ones(n, 1) a2] ; %5000x26
a3 = sigmoid(a2 * Theta2'); %5000x10
J = sum( sum( -y.* log(a3) - (1-y).*log(1-a3) ))/ m;
% pay attention :" Theta1(:,2:end) " , no "Theta1" .
regularized = lambda/(2*m) * (sum(sum(Theta1(:,2:end).^2)) + sum(sum(Theta2(:,2:end).^2)) );
J = J + regularized;

%part2

delta3 = a3 - y; %5000*10
delta2 = delta3 * Theta2; %5000*26
delta2 = delta2(:, 2 : end);
delta2 = delta2 .* sigmoidGradient(z2); %5000*25

Delta_1 = zeros(size(Theta1));
Delta_2 = zeros(size(Theta2));

Delta_1 = Delta_1 + delta2' * a1;
Delta_2 = Delta_2 + delta3' * a2;

Theta1_grad = ((1 / m) * Delta_1) + ((lambda / m) * Theta1);
Theta2_grad = ((1 / m) * Delta_2) + ((lambda / m) * Theta2);

Theta1_grad(:, 1) = Theta1_grad(:, 1) - ((lambda / m) * (Theta1(:, 1)));
Theta2_grad(:, 1) = Theta2_grad(:, 1) - ((lambda / m) * (Theta2(:, 1))); %这两行语句代表...
%Theta1_grad, Theta2_grad中第一列theta值不需要正则化
% -------------------------------------------------------------

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

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

end


坚持。
By 信念