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 networkTheta1 = 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 variablesm = 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;  %part2delta3 = a3 - y;  %5000*10delta2 = delta3 * Theta2;  %5000*26delta2 = delta2(:, 2 : end);delta2 = delta2 .* sigmoidGradient(z2);  %5000*25Delta_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 gradientsgrad = [Theta1_grad(:) ; Theta2_grad(:)];end

坚持。

By 信念