Machine Learning 线性回归( Linear Regression) Andrew Ng 课程练习 Matlab Script 详细解析

close all;

clear;

clc;

clf;

%该脚本尾部有原数据

% /media/heliheng/Resource/deep_learning/matMLLRex

X = load('ex2x.dat');

Y = load('ex2y.dat');

plot(X, Y, 'o');

ylabel('Height in meters')

xlabel('Age in years')

% store the number of training examples 训练样列的数目

m = length(Y);

% Add a column of ones to X 考虑到偏置项,加上一列ones(m,1),即m行1列的单位矩阵

X = [ones(m, 1), X];

%X m行2列 [mx2] the dimensions of the matrix X

theta = zeros(size(X(1,:)));

% theta <= theta 的转置

theta = theta';

%theta 2行1列 [2X1] the dimensions of the matrix theta

MAX_ITR = 1500;

alpha = 0.07;

for num_iterations = 1:MAX_ITR

grand = (1/m)*X'*(X*theta-Y);

theta = theta-alpha*grand;

end

theta

%%

% Plot the linear fit

% keep previous plot visible

hold on;

%X*theta = X0*theta0+X1*theta1+...+Xj*thetaj+...+Xm*thetam

plot(X(:,2), X*theta, '-')

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

% don't overlay any more plots on this figure

hold off

%%

% the predicted height

%the predicted height for age 3.5 predict1 : 年龄3.5的预测身高值

predict1= [1,3.5]*theta

%the predicted height for age 7 predict2 : 年龄7的预测身高值

predict2=[1,7]*theta

%%

% Calculate J matrix

% Grid over which we will calculate J

%-3到3之间的数值被100等分

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

%-1到1之间的数值被100等分

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

% initialize J_vals to a matrix of 0's

J_vals = zeros(length(theta0_vals), length(theta1_vals));

for i = 1:length(theta0_vals)

for j = 1:length(theta1_vals)

%T:[2X1] T=[-3;-1] or [-3;-0.979798] or ......[3;1] 等有100x100种取值；

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

% J_vals:[100X100]

J_vals(i,j) = (0.5/m) * (X *T- Y)'* (X * T - Y);

end

end

J_vals = J_vals';

% 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

% Surface plot

figure;

surf(theta0_vals, theta1_vals, J_vals)

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

figure;

% Plot the cost function with 15 contours spaced logarithmically

% between 0.01 and 100

%x=logspace(a,b,n)生成有n个元素的对数等分行向量x，且x(1)=10的a次方，x(n)=10的b次方；

%生成从10的a次方到10的b次方之间按对数等分的n个元素的行向量。n如果省略，则默认值为50

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

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

%{

X : [50x1] double

2.3684

2.5400

2.5421

2.5491

2.7867

2.9117

3.0356

3.1147

3.1582

3.3276

3.3793

3.4122

3.4216

3.5316

3.6393

3.6733

3.9256

4.0499

4.2483

4.3440

4.3827

4.4231

4.6102

4.6881

4.9777

5.0360

5.0685

5.4161

5.4396

5.4563

5.5698

5.6016

5.6878

5.7216

5.8539

6.1978

6.3511

6.4797

6.7384

6.8638

7.0223

7.0782

7.1514

7.4664

7.5974

7.7441

7.7730

7.8265

7.9306

Y : [50x1] double

0.7792

0.9160

0.9054

0.9057

0.9390

0.9668

0.9644

0.9145

0.9393

0.9607

0.8984

0.9121

0.9424

0.9662

1.0527

1.0144

0.9597

0.9685

1.0766

1.1455

1.0341

1.0070

0.9668

1.0896

1.0634

1.1237

1.0323

1.0874

1.0703

1.1606

1.0778

1.1070

1.0972

1.1649

1.1412

1.0844

1.1252

1.1168

1.1971

1.2069

1.1251

1.1236

1.2133

1.2523

1.2497

1.1800

1.1897

1.3030

1.2601

1.2562

%}