Coursera——Machine Learning （linear Regression) week2 编程作业答案
1、warmUpExercise.m：输出一个5*5的单位矩阵（identity matrix）
function A = warmUpExercise()
%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
在Octave中输入命令为：
2、plotData.m:绘制一个散点图
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.
figure; %打开一个新的图像窗口
% ====================== 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);
plot(x,y,'rx','MarkerSize',10);
ylabel('Profit in $10,000s');
xlabel('Population of City in 10,000s');
% ============================================================
end在Octave中命令为：
3、computeCost.m:计算单个变量下的代价函数J(θ)
computeCostMulti.m:计算多个变量下的代价函数J(θ)
这两种情况下的代码是相同的。
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); % 训练集样本个数
% 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.
J=1/(2*m)*sum((X*theta-y).^2);
% =========================================================================
end在Octave下命令为：X增加1列m行，值为1；初始化θ为2行1列，值为0
4、gradientDescent.m/gradientDescentMulti.m:梯度下降算法求θ最优解
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
% theta = GRADIENTDESCENT(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.
%
theta=theta-alpha*(1/m)*(X'*(X*theta-y));
% ============================================================
% Save the cost J in every iteration
J_history(iter) = computeCost(X, y, theta);
end
end
在octave下命令为：
5、featureNormalize.m:将特征进行缩放后的值
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.
%
for i=1:size(X,2)
mu(i)=mean(X(:,i)); %第i列所有元素的平均值
sigma(i)=std(X(:,i));
end
X_norm=(X_norm - mu) ./ sigma;
% ============================================================
end
在Octave下的命令为：
6、normalEqn.m:正规方程可以直接求θ的最优解
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=pinv(X'*X)*X'*y;
% -------------------------------------------------------------
% ============================================================
end
在Octave下命令为：
最后提交，
