随机梯度下降算法求解SVM

测试代码（ｍａｔｌａｂ）如下：

clear;
load E:\dataset\USPS\USPS.mat;
% data format:
% Xtr n1*dim
% Xte n2*dim
% Ytr n1*1
% Yte n2*1
% warning: labels must range from 1 to n, n is the number of labels
% other label values will make mistakes
u=unique(Ytr);
Nclass=length(u);

allw=[];allb=[];
step=0.01;C=0.1;
param.iterations=1;
param.lambda=1e-3;
param.biaScale=1;
param.t0=100;

tic;
for classname=1:1:Nclass
temp_Ytr=change_label(Ytr,classname);
[w,b] = sgd_svm(Xtr,temp_Ytr, param);
allw=[allw;w];
allb=[allb;b];
fprintf('class %d is done \n', classname);
end

[accuracy predict_label]=my_svmpredict(Xte, Yte, allw, allb);
fprintf(' accuracy is %.2f percent.\n' , accuracy*100 );
toc;

function [temp_Ytr] = change_label(Ytr,classname)
temp_Ytr=Ytr;
tep2=find(Ytr~=classname);
tep1=find(Ytr==classname);
temp_Ytr(tep2)=-1;
temp_Ytr(tep1)= 1;

function [true_W,b]=sgd_svm(X,Y,param)
% input:
% X is n*dim
% Y is n*1 (label is 1 or 0)
% output:
% true_W is dim*1 ,so the score is X*W'+b
% b is 1*1 number
iterations=param.iterations;%10
lambda=param.lambda;%1e-3
biaScale=param.biaScale;%0
t0=param.t0;%100
t=t0;

w=zeros(1,size(X,2));
bias=0;

for k=1:1:iterations
for i=1:1:size(X,1)
t=t+1;
alpha = (1.0/(lambda*t));
if(Y(i)*(X(i,:)*w'+bias)<1)
bias=bias+alpha*Y(i)*biaScale;
w=w+alpha*Y(i,1).*X(i,:);
end
end
end
b=bias;
true_W=w;

function [accuracy predict_label]=my_svmpredict(Xte, Yte, allw, allb)
% allw is nclass * dim
% allb is nclass * 1
% Yte must range from 1 to nclass, other label values will make mistakes
score = Xte * allw'+repmat(allb',[size(Bte,1),1]);
[bb c]=sort(score,2,'descend');
predict_label=c(:,1);
temp = predict_label((predict_label-Yte)==0);
right=size( temp,1 );
accuracy=right/size(Yte,1);