机器学习第2周编程作业
2016-07-27 22:25
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function A = warmUpExercise() %生成5*5的单位矩阵 %WARMUPEXERCISE Example function in octave % A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix A = []; % ============= YOUR CODE HERE ============== % Instructions: Return the 5x5 identity matrix % In octave, we return values by defining which variables % represent the return values (at the top of the file) % and then set them accordingly. A = eye(5); % =========================================== end function plotData(x, y) %画图 %PLOTDATA Plots the data points x and y into a new figure % PLOTDATA(x,y) plots the data points and gives the figure axes labels of % population and profit. % ====================== YOUR CODE HERE ====================== % Instructions: Plot the training data into a figure using the % "figure" and "plot" commands. Set the axes labels using % the "xlabel" and "ylabel" commands. Assume the % population and revenue data have been passed in % as the x and y arguments of this function. % % Hint: You can use the 'rx' option with plot to have the markers % appear as red crosses. Furthermore, you can make the % markers larger by using plot(..., 'rx', 'MarkerSize', 10); figure; % open a new figure window plot(x,y,'rx', 'MarkerSize', 10); xlabel('population'); ylabel('revenue'); % ============================================================ end function J = computeCost(X, y, theta) %计算J,同computeCostMulti.m,可用于多元线性回归 %COMPUTECOST Compute cost for linear regression % J = COMPUTECOST(X, y, theta) computes the cost of using theta as the % parameter for linear regression to fit the data points in X and y % Initialize some useful values m = length(y); % number of training examples % You need to return the following variables correctly J = 0; % ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta % You should set J to the cost. predictions = X*theta; sqr = (predictions-y).^2; J = 1/(2*m)*sum(sqr); % ========================================================================= end function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters) %梯度下降,同gradientDescentMulti.m,可用于多元线性回归 %GRADIENTDESCENT Performs gradient descent to learn theta % theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by % taking num_iters gradient steps with learning rate alpha % Initialize some useful values m = length(y); % number of training examples J_history = zeros(num_iters, 1); for iter = 1:num_iters % ====================== YOUR CODE HERE ====================== % Instructions: Perform a single gradient step on the parameter vector % theta. % % Hint: While debugging, it can be useful to print out the values % of the cost function (computeCost) and gradient here. % predictions = X*theta; theta = theta - alpha/m.*((predictions-y)'*X)'; % ============================================================ % Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta); end end function [X_norm, mu, sigma] = featureNormalize(X) %特征缩放 %FEATURENORMALIZE Normalizes the features in X % FEATURENORMALIZE(X) returns a normalized version of X where % the mean value of each feature is 0 and the standard deviation % is 1. This is often a good preprocessing step to do when % working with learning algorithms. % You need to set these values correctly X_norm = X; mu = zeros(1, size(X, 2)); sigma = zeros(1, size(X, 2)); % ====================== YOUR CODE HERE ====================== % Instructions: First, for each feature dimension, compute the mean % of the feature and subtract it from the dataset, % storing the mean value in mu. Next, compute the % standard deviation of each feature and divide % each feature by it's standard deviation, storing % the standard deviation in sigma. % % Note that X is a matrix where each column is a % feature and each row is an example. You need % to perform the normalization separately for % each feature. % % Hint: You might find the 'mean' and 'std' functions useful. % mu = mean(X); sigma = std(X); X_norm = (X-mu)/diag(sigma); % ============================================================ end function [theta] = normalEqn(X, y) %正规方程 %NORMALEQN Computes the closed-form solution to linear regression % NORMALEQN(X,y) computes the closed-form solution to linear % regression using the normal equations. theta = zeros(size(X, 2), 1); % ====================== YOUR CODE HERE ====================== % Instructions: Complete the code to compute the closed form solution % to linear regression and put the result in theta. % % ---------------------- Sample Solution ---------------------- theta = pinv(X'*X)*X'*y; % ------------------------------------------------------------- % ============================================================ end
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