斯坦福机器学习实验之1-单变量线性回归(Linear Regression with One Variable)

1.数据图形化(Plotting the Data)

在进行任务之前，将数据可视化对我们理解数据很有用。
1)载入数据
函数: load;length

data = load('ex1data1.txt'); % read comma separated dataX = data(:, 1); y = data(:, 2);m = length(y); % number of training examples

2)可视化数据:plotData.m
函数：figure；plot；title；xlabel;ylabel

figureplot(x,y,'Color','g','LineStyle','none','Marker','x','MarkerSize',10); % Plot the datatitle('plotData');xlabel('Population of City in 10,000s'); %Set the x-axis labelylabel('Profit in $10,000s'); % Set the y-axis label

2.梯度下降(Gradient Descent)

1)准备参数
函数：ones;zeros;

X = [ones(m, 1), data(:,1)]; % Add a column of ones to xtheta = zeros(2, 1); % initialize fitting parametersiterations = 1500;alpha = 0.01;

2)计算代价函数(Computing the cost):computeCost.m
函数：sum
运算符： . ^

function J = computeCost(X,y,theta)%myFun - Description% Long description% square every elements in matrix A : A .^2m = length(y); % number of training examplesh=X*theta;J=1/(2*m)*sum((h-y).^2);end

3.梯度下降

gradientDescent.m

% for i=1:10,%   v(i)=2^i;% end;function [theta,J_history] = gradientDescent(X,y,theta,alpha,iterations)   m=length(y);   theta_s=theta;   for i=1:iterations,      theta(1)=theta(1)-alpha/m*sum(X*theta_s-y);     theta(2)=theta(2)-alpha/m*sum((X*theta_s-y).*X(:,2));     theta_s=theta;     % Save the cost in every iteration     J_history(iterations)=computeCost(X,y,theta);   end   J_historyend

说明：用theta_s保留计算结果；分别计算theta(1)和theta(2),原因是theta为两行向量，而X和y都是m行矩阵，维度不匹配。

4.调试

1)matlab向量编号是从1开始的；
2)运算时注意维度的匹配。