smo for classification-优快云博客

本文详细介绍了SMO算法的工作原理及其在支持向量机中的应用，并提供了具体的MATLAB实现代码示例。通过该示例可以了解到SMO算法如何通过迭代优化求解拉格朗日乘子来找到最优分类超平面。

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function [a,b]=smo(x,y,c,tol,max_passes)
num=size(x,2);
a=zeros(num,1);b=0;
passes=0;
e=zeros(num,1);
while passes<max_passes
    num_changed_alphas=0;
    for i=1:num
        f2=0;
        for k=1:num
            f2=f2+a(k)*y(k)*(x(:,k)'*x(:,i));
        end
        f2=f2+b;
        e(i)=f2-y(i);
        if y(i)*e(i)<-tol&&a(i)<c || y(i)*e(i)>tol&&a(i)>0
            j=ceil(rand(1,1)*num);
            while j==i
                j=ceil(rand(1,1)*num);
            end
            ai_old=a(i);aj_old=a(j);
            f=0;
            for k=1:num
                f=f+a(k)*y(k)*(x(:,k)'*x(:,j));
            end
            f=f+b; e(j)=f-y(j);
            if y(i)~=y(j)
                L=max(0,a(j)-a(i));
                H=min(c,c+a(j)-a(i));
            else
                L=max(0,a(i)+a(j)-c);
                H=min(c,a(i)+a(j));
            end
            if L==H
                continue;
            end
            eta=2*x(:,i)'*x(:,j)-x(:,i)'*x(:,i)-x(:,j)'*x(:,j);
            if eta>=0
                continue
            end
            a(j)=a(j)-y(j)*(e(i)-e(j))/eta;
            if a(j)>H
                a(j)=H;
            elseif a(j)<L
                a(j)=L;
            end
            if a(j)-aj_old<1e-5
                continue
            end
            a(i)=a(i)+y(i)*y(j)*(aj_old-a(j));
            b1=b-e(i)-y(i)*(a(i)-ai_old)*(x(:,i)'*x(:,i))-y(j)*(a(j)-aj_old)*(x(:,i)'*x(:,j));
            b2=b-e(j)-y(i)*(a(i)-ai_old)*(x(:,i)'*x(:,j))-y(j)*(a(j)-aj_old)*(x(:,j)'*x(:,j));
            if a(i)>0&&a(i)<c
                b=b1;
            elseif a(j)>0&&a(j)<c
                b=b2;
            else
                b=(b1+b2)/2;
            end
            num_changed_alphas=num_changed_alphas+1;
        end
    end
    if num_changed_alphas==0
        passes=passes+1;
    else
        passes=0;
    end
end
end

function predict=smopredict(a,b,x,y,test)
num=max(size(a,1),size(a,2));
f=zeros(1,size(test,2));
for i=1:num
    f=f+a(i)*y(i)*x(:,i)'*test;
end
f=f+b;
predict=-ones(1,size(test,2));
predict=predict+2*(f>0);
end

x=[0.9,0.8,0.7,0.2,0.1,0.1,0.2;0.1,0.2,0.1,0.9,0.7,0.99,0.777];
y=[1,1,1,-1,-1,-1,-1];
[a,b]=smo(x,y,1,1e-3,100);
test=[0.9,0.7,0.6,0.1,0.3,0.2,0;0.1,0.2,0.1,0.9,0.8,0.7,0.88];
predict=smopredict(a,b,x,y,test)