版权声明:本文为博主原创文章,未经博主允许不得转载。 https://blog.csdn.net/q__y__L/article/details/72614661
机器学习经典算法SVM,网上有各种博客介绍,以及各种语言的源代码。 这里提供SVM几种版本的matlab实现,主要目的是熟悉利用CVX来求解凸优化问题。
basic SVM
推导什么的就不说了,直接搬最后的公式:
minw,b2∥w∥22
s.t.yi(wTxi+b)≥1,i=1,...,L
然后是代码:`
function [ w,b ] = svm_prim_sep( data,labels )
%UNTITLED2 此处显示有关此函数的摘要
% Input:
% data: num-by-dim matrix .mun is the number of data points,
% dim is the the dimension of a point
% labels: num-by-1 vector, specifying the class that each point belongs
% to +1 or -1
% output:
% w: dim-by -1 vector ,the mormal dimension of hyperpalne
% b: a scalar, the bias
[num,dim]=size(data);
cvx_begin
variables w(dim) b;
minimize (norm(w));
subject to
labels.*(data*w+b)>=1;
cvx_end
end
然后随便随机生成了10个2维样本,运行结果如下:
- Soft Margin SVM
Soft Margin SVM
线性不可分的时候,通过引入罚函数(penalty function)来解决,使得分类误差最小。公式如下:
代码依然很简单:
function [ w,b ] = svm_prim_sep( data,labels )
%UNTITLED2 此处显示有关此函数的摘要
% Input:
% data: num-by-dim matrix .mun is the number of data points,
% dim is the the dimension of a point
% labels: num-by-1 vector, specifying the class that each point belongs
% to +1 or -1
% output:
% w: dim-by -1 vector ,the mormal dimension of hyperpalne
% b: a scalar, the bias
[num,dim]=size(data);
cvx_begin
variables w(dim) b,xi(num);
minimize (sum(w.^2)/2+C * sum(xi.^2));
subject to
labels.* (data * w+b)>=1-xi;
xi>=0;
cvx_end
end
是不是很简单?例子以后再给吧。(公式乱码,请尝试其它浏览器)
未完待续,