Coursera Machine Learning 第四周 quiz Programming Exercise 3 Multi-class Classification and Neural
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lrCostFunction.m
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)%% =============================================================sigm = sigmoid(X*theta); J = sum(-y.*log(sigm) - (1-y).*log(1-sigm))/m + lambda * sum(theta(2:end).^2)/(2*m); grad = X' * (sigm-y)/m; grad0 = grad(1); grad = grad + (lambda/m)*theta; grad(1) = grad0; grad = grad(:);endoneVsAll.m
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% logisitc 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 use % 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 k=1:num_labels initial_theta = zeros(n + 1, 1); options = optimset('GradObj', 'on', 'MaxIter', 50); [theta] = fmincg (@(t)(lrCostFunction(t, X, (y == k), lambda)),initial_theta, options); all_theta(k,:) = theta'; end endpredictOneVsAll.m
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.% % =========================================================================[c,i] = max(sigmoid(X * all_theta'), [], 2); p = i; endpredict.m
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.%X = [ones(m, 1) X]; z2 = Theta1 * X'; a2 = sigmoid(z2); a2 = [ones(1, m);a2]; z3 = Theta2 * a2; a3 = sigmoid(z3); output =a3'; [c,i] = max(output, [], 2); p = i; % =========================================================================end
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