斯坦福《机器学习》课程算法matlab实现之梯度下降算法——直线回归（一）

梯度下降算，可用于回归，也可用于分类，下面是该算法的最简单的演示，学习率alpha对算法的收敛影响很大，取大了不收敛，过小过大迭代次数增加；

clear;clc;
data=genlineardata(13,-3.36,100);%生成在直线y=13-3.36*x周围的100个点存入data[100*3],data第一列全为1

theta=zeros(2,1);

theta(1)=0;

theta(2)=1;

times=0;

alpha=0.1;

h=0;

distant=0;

sum0=0;

sum1=0;

[row,col]=size(data);

figure;

plot(data(:,2),data(:,3),'r.');

x=-5:5;

switch(3)

case 1,

% stochastic gradient descent.

while(1)

y=theta(2)*x+theta(1);

hold on;

plot(x,y,'r');

temp0=theta(1);

temp1=theta(2);

for i=1:row

h=theta(1)+theta(2)*data(i,2);

alpha=0.2/i;

sum0=(data(i,3)-h);

sum1=(data(i,3)-h)*data(i,2);

theta(1)=theta(1)+alpha*sum0;

theta(2)=theta(2)+alpha*sum1;

end

distant=abs(theta(1)-temp0)+abs(theta(2)-temp1);

if(distant<0.001)

break;

end

times=times+1;

if(times>20)

break;

end

end

case 2,

% batch gradient descent.

while(1)

y=theta(2)*x+theta(1);

hold on;

plot(x,y,'r');

temp0=theta(1);

temp1=theta(2);

sum0=0;

sum1=0;

times=times+1;

alpha=1/(times*row);

for i=1:row

h=theta(1)+theta(2)*data(i,2);

sum0=sum0+alpha*(data(i,3)-h);

sum1=sum1+alpha*(data(i,3)-h)*data(i,2);

end

theta(1)=theta(1)+sum0;

theta(2)=theta(2)+sum1/2;

distant=abs(theta(1)-temp0)+abs(theta(2)-temp1);

if(distant<0.001)

break;

end

if(times>20)

break;

end

end

case 3,

%Least squares revisited

y=theta(2)*x+theta(1);

hold on;

plot(x,y,'r');

X=data(:,1:2);

Y=data(:,3);

theta=(X'*X)\X'*Y;

end

theta(1)

theta(2)

times

y=theta(2)*x+theta(1);

hold on;

plot(x,y,'g');

% times