machine learning ng week 2 program code

在Coursera上学习了两周的Machine Learning课程，第二周开始学习使用Octave，以下是Week 2的编程作业代码：

1. warmUpExercise.m

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function  = warmUpExercise()

%   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

1. plotData.m

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   function plotData(x, y) %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); % Plot the data ylabel('Profit in $10,000s'); % Set the y−axis label xlabel('Population of City in 10,000s'); % Set the x−axis label % ============================================================ end

2. computeCost.m

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   function J = computeCost(X, y, theta) %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. temp = sum((X * theta - y).^2); J = temp / (2 * m); % ========================================================================= end

3. gradientDescent.m

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   function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters) %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. % tempTheta = theta; theta(1) = tempTheta(1) - alpha / m * sum(X * tempTheta - y); theta(2) = tempTheta(2) - alpha / m * sum((X * tempTheta - y) .* X(:,2)); % ============================================================ % Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta); end end

4. featureNormalize.m

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   function [X_norm, mu, sigma] = featureNormalize(X) %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. % featureNumber = size(X, 2)； for i = 1 : featureNumber mu(i) = mean(X(:,i)); %计算每个特征的平均值 sigma(i) = std(X(:,i)); %计算每个特征的标准差 X_norm(:,i) = (X(:,i) - mu(i)) / sigma(i); end % ============================================================ end

5. computeCostMulti

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   function J = computeCostMulti(X, y, theta) %COMPUTECOSTMULTI Compute cost for linear regression with multiple variables % J = COMPUTECOSTMULTI(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. temp = sum(((X * theta - y).^2)); J = 1 / (2*m) * temp; % ========================================================================= end

6. gradientDescentMulti.m

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   function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters) %GRADIENTDESCENTMULTI Performs gradient descent to learn theta % theta = GRADIENTDESCENTMULTI(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 (computeCostMulti) and gradient here. % tempTheta = theta; featureNumber = size(X,2); for i = 1 : featureNumber theta(i) = tempTheta(i) - alpha / m * sum((X * tempTheta - y) .* X(:,i)); end % ============================================================ % Save the cost J in every iteration J_history(iter) = computeCostMulti(X, y, theta); end end

7. normalEqn.m

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   function [theta] = normalEqn(X, y) %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 = (X' * X) X' * y; % ------------------------------------------------------------- % ============================================================ end