转行程序员1 机器学习 线性回归 Linear Regression 纯属敦促自己学习

主要学习了Andrew Ng的公开课 machine learning 之Linear Regression，其exercise网址如下
http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex2/ex2.html
编写的代码如下：

%%%%%%%%%%%%%%%%%%%%%%%%Linear regression

clear all; close all; clc

x = load('ex2x.dat');

y = load('ex2y.dat');

figure % open a new figure window

plot(x, y, 'o');

ylabel('Height in meters')

xlabel('Age in years')

m = length(y); % store the number of training examples 样本数量

x = [ones(m, 1), x]; % Add a column of ones to x  

theta=zeros(2,1);

alpha=0.07;% learning rate

for inter=1:1500 % 迭代次数

    h_theta=x*theta;

    theta=theta-alpha/m*x'*(h_theta-y);

end

hold on % Plot new data without clearing old plot

plot(x(:,2), x*theta, '-') % remember that x is now a matrix with 2 columns

                           % and the second column contains the time info

legend('Training data', 'Linear regression')

%%%%%%%%%%%%%%%%%%%%%%%%  Understanding J(theta)

J_vals = zeros(100, 100);   % initialize Jvals to 100x100 matrix of 0's

theta0_vals = linspace(-3, 3, 100);

theta1_vals = linspace(-1, 1, 100);

for i = 1:length(theta0_vals)

      for j = 1:length(theta1_vals)

      t = [theta0_vals(i); theta1_vals(j)];

      J_vals(i,j) = 1/2/m*sum((theta0_vals(i)+theta1_vals(j)*x(:,2)-y(:)).^2);

    end

end

% Plot the surface plot

% Because of the way meshgrids work in the surf command, we need to

% transpose J_vals before calling surf, or else the axes will be flipped

J_vals = J_vals';

figure;

surf(theta0_vals, theta1_vals, J_vals)

xlabel('\theta_0'); ylabel('\theta_1')

% Plot the cost function with 15 contours spaced logarithmically

% between 0.01 and 100

figure;

contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 2, 15))

xlabel('\theta_0'); ylabel('\theta_1')