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Specifically, we will try to learn a function of the form:
The function σ(z)≡11+exp(−z) is often called the “sigmoid” or “logistic” function
我们只需要计算y=1的概率就ok了。其Cost Function如下:
J(θ)=−∑i(y(i)log(hθ(x(i)))+(1−y(i))log(1−hθ(x(i)))).
除了方程不一样,其他的计算和Linear Regression是完全一样的。
OK,接下来我们来看看练习怎么做。
addpath ../commonaddpath ../common/minFunc_2012/minFuncaddpath ../common/minFunc_2012/minFunc/compiled% Load the MNIST data for this exercise.% train.X and test.X will contain the training and testing images.% Each matrix has size [n,m] where:% m is the number of examples.% n is the number of pixels in each image.% train.y and test.y will contain the corresponding labels (0 or 1).binary_digits = true;[train,test] = ex1_load_mnist(binary_digits);% Add row of 1s to the dataset to act as an intercept term.train.X = [ones(1,size(train.X,2)); train.X]; test.X = [ones(1,size(test.X,2)); test.X];% Training set dimensionsm=size(train.X,2);n=size(train.X,1);% Train logistic regression classifier using minFuncoptions = struct('MaxIter', 100);% First, we initialize theta to some small random values.theta = rand(n,1)*0.001;% Call minFunc with the logistic_regression.m file as the objective function.%% TODO: Implement batch logistic regression in the logistic_regression.m file!%%tic;%theta=minFunc(@logistic_regression, theta, options, train.X, train.y);%fprintf('Optimization took %f seconds.\n', toc);% Now, call minFunc again with logistic_regression_vec.m as objective.%% TODO: Implement batch logistic regression in logistic_regression_vec.m using% MATLAB's vectorization features to speed up your code. Compare the running% time for your logistic_regression.m and logistic_regression_vec.m implementations.%% Uncomment the lines below to run your vectorized code.%theta = rand(n,1)*0.001;tic;theta=minFunc(@logistic_regression_vec, theta, options, train.X, train.y);fprintf('Optimization took %f seconds.\n', toc);% Print out training accuracy.tic;accuracy = binary_classifier_accuracy(theta,train.X,train.y);fprintf('Training accuracy: %2.1f%%\n', 100*accuracy);% Print out accuracy on the test set.accuracy = binary_classifier_accuracy(theta,test.X,test.y);fprintf('Test accuracy: %2.1f%%\n', 100*accuracy);
function [f,g] = logistic_regression(theta, X,y) % % Arguments: % theta - A column vector containing the parameter values to optimize. % X - The examples stored in a matrix. % X(i,j) is the i'th coordinate of the j'th example. % y - The label for each example. y(j) is the j'th example's label. % m=size(X,2); n=size(X,1); % initialize objective value and gradient. f = 0; g = zeros(size(theta)); % % TODO: Compute the objective function by looping over the dataset and summing % up the objective values for each example. Store the result in 'f'. % % TODO: Compute the gradient of the objective by looping over the dataset and summing % up the gradients (df/dtheta) for each example. Store the result in 'g'. %%%% YOUR CODE HERE %%%% Step 1?Compute Cost Functionfor i = 1:m f = f - (y(i)*log(sigmoid(theta' * X(:,i))) + (1-y(i))*log(1-... sigmoid(theta' * X(:,1))));endfor j = 1:n for i = 1:m g(j) = g(j) + X(j,i)*(sigmoid(theta' * X(:,i)) - y(i)); end end
function [train, test] = ex1_load_mnist(binary_digits) % Load the training data X=loadMNISTImages('train-images-idx3-ubyte'); % 784x60000 60000张图片28x28pixel y=loadMNISTLabels('train-labels-idx1-ubyte')'; % 1*60000 if (binary_digits) % Take only the 0 and 1 digits X = [ X(:,y==0), X(:,y==1) ]; %通过y==0和y==1直接得到y=0和1的index y = [ y(y==0), y(y==1) ]; end % Randomly shuffle the data I = randperm(length(y)); y=y(I); % labels in range 1 to 10 X=X(:,I); % We standardize the data so that each pixel will have roughly zero mean and unit variance. s=std(X,[],2); %??std??X??? m=mean(X,2); X=bsxfun(@minus, X, m); X=bsxfun(@rdivide, X, s+.1); % 就是计算(x-m)/s 加0.1是为了防止分母为0 % Place these in the training set train.X = X; train.y = y; % Load the testing data X=loadMNISTImages('t10k-images-idx3-ubyte'); y=loadMNISTLabels('t10k-labels-idx1-ubyte')'; if (binary_digits) % Take only the 0 and 1 digits X = [ X(:,y==0), X(:,y==1) ]; y = [ y(y==0), y(y==1) ]; end % Randomly shuffle the data I = randperm(length(y)); y=y(I); % labels in range 1 to 10 X=X(:,I); % Standardize using the same mean and scale as the training data. X=bsxfun(@minus, X, m); X=bsxfun(@rdivide, X, s+.1); % Place these in the testing set test.X=X; test.y=y;【说明:本文为原创文章,转载请注明出处:blog.csdn.net/songrotek 欢迎交流QQ:363523441】