machine-learning-ex3

coursera machine-learning-ex3 课程作业记录

Multi-class Classification and Neural Networks

function [J, grad] = lrCostFunction(theta, X, y, lambda)%LRCOSTFUNCTION Compute cost and gradient for logistic regression with %regularization%   J = LRCOSTFUNCTION(theta, X, y, lambda) computes the cost of using%   theta as the parameter for regularized logistic regression and the%   gradient of the cost w.r.t. to the parameters. % Initialize some useful valuesm = length(y); % number of training examples% You need to return the following variables correctly J = 0;grad = zeros(size(theta));% ====================== YOUR CODE HERE ======================% Instructions: Compute the cost of a particular choice of theta.%               You should set J to the cost.%               Compute the partial derivatives and set grad to the partial%               derivatives of the cost w.r.t. each parameter in theta%% Hint: The computation of the cost function and gradients can be%       efficiently vectorized. For example, consider the computation%%           sigmoid(X * theta)%%       Each row of the resulting matrix will contain the value of the%       prediction for that example. You can make use of this to vectorize%       the cost function and gradient computations. %% Hint: When computing the gradient of the regularized cost function, %       there're many possible vectorized solutions, but one solution%       looks like:%           grad = (unregularized gradient for logistic regression)%           temp = theta; %           temp(1) = 0;   % because we don't add anything for j = 0  %           grad = grad + YOUR_CODE_HERE (using the temp variable)%hx=sigmoid(X*theta);J=1/m*(-y'*log(hx)-(1-y)'*log(1-hx))+lambda/2/m*theta(2:end)'*theta(2:end);grad=1/m*X'*(hx-y)+lambda/m*theta;grad(1)=grad(1)-lambda/m*theta(1);% =============================================================grad = grad(:);end

function [all_theta] = oneVsAll(X, y, num_labels, lambda)%ONEVSALL trains multiple logistic regression classifiers and returns all%the classifiers in a matrix all_theta, where the i-th row of all_theta %corresponds to the classifier for label i%   [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels%   logistic regression classifiers and returns each of these classifiers%   in a matrix all_theta, where the i-th row of all_theta corresponds %   to the classifier for label i% Some useful variablesm = size(X, 1);n = size(X, 2);% You need to return the following variables correctly all_theta = zeros(num_labels, n + 1);% Add ones to the X data matrixX = [ones(m, 1) X];% ====================== YOUR CODE HERE ======================% Instructions: You should complete the following code to train num_labels%               logistic regression classifiers with regularization%               parameter lambda. %% Hint: theta(:) will return a column vector.%% Hint: You can use y == c to obtain a vector of 1's and 0's that tell you%       whether the ground truth is true/false for this class.%% Note: For this assignment, we recommend using fmincg to optimize the cost%       function. It is okay to use a for-loop (for c = 1:num_labels) to%       loop over the different classes.%%       fmincg works similarly to fminunc, but is more efficient when we%       are dealing with large number of parameters.%% Example Code for fmincg:%%     % Set Initial theta%     initial_theta = zeros(n + 1, 1);%     %     % Set options for fminunc%     options = optimset('GradObj', 'on', 'MaxIter', 50);% %     % Run fmincg to obtain the optimal theta%     % This function will return theta and the cost %     [theta] = ...%         fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), ...%                 initial_theta, options);%for c=1:num_labelsinitial_theta=zeros(n+1,1);options=optimset('GradObj','on','MaxIter',50);[theta]=fmincg(@(t)lrCostFunction(t,X,(y==c),lambda),initial_theta,options);all_theta(c,:)=theta';end% =========================================================================end

function p = predictOneVsAll(all_theta, X)%PREDICT Predict the label for a trained one-vs-all classifier. The labels %are in the range 1..K, where K = size(all_theta, 1). %  p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions%  for each example in the matrix X. Note that X contains the examples in%  rows. all_theta is a matrix where the i-th row is a trained logistic%  regression theta vector for the i-th class. You should set p to a vector%  of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2%  for 4 examples) m = size(X, 1);num_labels = size(all_theta, 1);% You need to return the following variables correctly p = zeros(size(X, 1), 1);% Add ones to the X data matrixX = [ones(m, 1) X];% ====================== YOUR CODE HERE ======================% Instructions: Complete the following code to make predictions using%               your learned logistic regression parameters (one-vs-all).%               You should set p to a vector of predictions (from 1 to%               num_labels).%% Hint: This code can be done all vectorized using the max function.%       In particular, the max function can also return the index of the %       max element, for more information see 'help max'. If your examples %       are in rows, then, you can use max(A, [], 2) to obtain the max %       for each row.%       [h,p]=max(X*all_theta',[],2);% =========================================================================end

function p = predict(Theta1, Theta2, X)%PREDICT Predict the label of an input given a trained neural network%   p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the%   trained weights of a neural network (Theta1, Theta2)% Useful valuesm = size(X, 1);num_labels = size(Theta2, 1);% You need to return the following variables correctly p = zeros(size(X, 1), 1);% ====================== YOUR CODE HERE ======================% Instructions: Complete the following code to make predictions using%               your learned neural network. You should set p to a %               vector containing labels between 1 to num_labels.%% Hint: The max function might come in useful. In particular, the max%       function can also return the index of the max element, for more%       information see 'help max'. If your examples are in rows, then, you%       can use max(A, [], 2) to obtain the max for each row.%a2=sigmoid(Theta1*[ones(1,m);X']);a3=sigmoid(Theta2*[ones(1,size(a2,2));a2]);[hx,p]=max(a3,[],1);p=p';% =========================================================================end