IRWLS-SVR-code.rar_IRWLS_SVR matlab_svr matlab_加权向量机_迭代加权

function [nsv,al3,bi,T,Lp]=irwls1(x,y,ker,C,epsi,par,tol); % % % This function solves the Support Vector Machine for regression. % % [nsv,al3,bi,T,Lp]=irwls1(x,y,ker,C,epsi,par,tol); % % This function solves the SVM using the IRWLS procedure. % Parameters: % % x: matrix of input vectors. Each row of x1 represents a d-dimensional vector. % The number of rows is the number of training samples. % y: column vector of the targets values. Each row represent the taerget of each sample in x. % ker: the kernel to be employed. It has to be a string out of: 'linear', 'poly_h', 'poly_i' and 'rbf'. % Type help kernel for further information. % C: is the penalty factor of the SVM soft-margin formulation. % epsi: is the epsilon insensitive zone defined arround the regression estimate. % par: is the parameter of the used kernel. type help kernel for further information. % tol: tolerance for the value of Lp, the primal functional, to stop the algorithm. % The default value if 10^-5. (optional) % % Outputs: % % nsv: number of support vector. % al3: the value of the alphas-alpha*. % bi: the value of the bias. % T: running time. % Lp: A vector that show the value of the primal \|w\|^2+C\sum_{i=0}^n \xi_i in each iteration % of the algorithm.% % Examples: % % with linear kernel % x=rand(20,1); % y=2*x+2+.2*randn(size(x)); % [nsv,alpha,bias]=irwls1(x,y,'linear',10,0.1); % svrplot(x,y,'linear',alpha,bias,0.1); % % W=x'*alpha; % X_test=rand(200,1); % Y_test=2*X_test+2+.2*randn(size(X_test)); % Output=X_test*W+bias; % Error=Y_test-Output; % % % with nonlinear (RBF) kernel: % x=10*(rand(100,1)-.5); % y=sinc(x)+.1*randn(size(x)); % [nsv,alpha,bias]=irwls1(x,y,'rbf',10,.05,0.5); % svrplot(x,y,'rbf',alpha,bias,0.05,0.5); % % X_test=10*(rand(1000,1)-.5); % Y_test=sinc(X_test)+.1*randn(size(X_test)); % Output=kernel('rbf',X_test,x(find(alpha),:),0.5)*alpha(find(alpha))+bias; % Error=Y_test-Output; % % Author: Fernando Perez-Cruz (fernandop@ieee.org) % Version: 1.0 % Date: 18th March 2002. % % T=clock; if (nargin<5 | nargin>7) %判断输入参数的个数 help irwls1 else if(nargin==5 & ker(1)=='p') disp('The used kernel needs an input parameter. We have set it to 2.'); % 多项式核par=2 par=2; elseif(nargin==5 & ker(1)=='r') fprintf(1,'The used kernel needs an input parameter. We have set it to %1.3f\n',sqrt(size(x,2))); %RBF核 par=x的列数开根号 par=sqrt(size(x,2)); elseif(nargin==5) % 没有核 par=0; end if(nargin<7) tol=10^-5; %固定tol end K=10^6; % N=size(x,1); % x的行数即输入向量的个数 ns=-1; k=2; hacer=1; bi=0; H=kernel(ker,x,x,par); i1p=1:2:N; %1,3,5，N i1n=2:2:N; %2,4,6，N-1 i1=[i1p i1n]; % i1=[1,3,5,...,2,4,6,...] a=zeros(N,1); a(i1)=C; al3=zeros(N,1); i2p=[]; i2n=[]; Lp(1)=N*C; e=y; while(hacer) al3_a=al3; bi_a=bi; al3=zeros(N,1); al3(i2p)=C; % al3(i2n)=-C; % if(length(i1)) Xi=inv([H(i1,i1)+diag(1./(a(i1))) ones(length(i1),1);ones(1,length(i1)) 0]); E=ones(N,1); E(i1n)=-1; aux=Xi*[y(i1)-E(i1)*epsi+C*H(i1,i2n)*ones(length(i2n),1)-C*H(i1,i2p)*ones(length(i2p),1);C*length(i2n)-C*length(i2p)]; al3(i1)=aux(1:length(i1)); bi=aux(length(i1)+1); end e_a=e; I=find(al3-al3_a); if(length(I)) e=e_a-H(:,I)*(al3(I)-al3_a(I))-(bi-bi_a); end Lp(k)=al3'*H*al3/2+C*sum(abs(e(find(abs(e)>epsi)))-epsi); if((abs(Lp(k)-Lp(k-1))/Lp(k-1))<tol & k>(ns+1)) nsv=length(i1)+length(i2n)+length(i2p); hacer=0; else if((Lp(k)-Lp(k-1))/Lp(k-1)>tol) LL=Lp(k-1); HH=Lp(k); posL=0; posH=1; while(posL==0) jj=(posH+posL)/2; al3b=al3*jj+al3_a*(1-jj); bib=bi*jj+bi_a*(1-jj); I=find(al3b-al3_a); if(length(I)) eb=e_a-H(:,I)*(al3b(I)-al3_a(I))-(bib-bi_a); end if(HH>LL) HHa=HH; posHa=posH; HH=al3b'*H*al3b/2+C*sum(abs(eb(find(abs(eb)>epsi)))-epsi); posH=jj; else LL=al3b'*H*al3b/2+C*sum(abs(eb(find(abs(eb)>epsi)))-epsi); posL=jj; end end jj=posH+posL; al3b=al3*jj+al3_a*(1-jj); bib=bi*jj+bi_a*(1-jj); I=find(al3b-al3_a); if(length(I)) eb=e_a-H(:,I)*(al3b(I)-al3_a(I))-(bib-bi_a); end valor=al3b'*H*al3b/2+C*sum(abs(eb(find(abs(eb)>epsi)))-epsi); posL=posH; LL=HH; posH=jj; HH=valor; if(valor>Lp(k-1)) while(abs(valor-Lp(k-1))/Lp(k-1)>10^-3) jj=(posH+posL)/2; al3b=al3*jj+al3_a*(1-jj); bib=bi*jj+bi_a*(1-jj); I=find(al3b-al3_a); if(length(I)) eb=e_a-H(:,I)*(al3b(I)-al3_a(I))-(bib-bi_a); end valor=al3b'*H*al3b/2+C*sum(abs(eb(find(abs(eb)>epsi)))-epsi); if(valor>Lp(k-1)) HH=valor; posH=jj; else LL=valor; posL=jj; end end end pos=jj; al3=al3*pos+al3_a*(1-pos); bi=bi*pos+bi_a*(1-pos); I=find(al3-al3_a); if(length(I)) e=e_a-H(:,I)*(al3(I)-al3_a(I))-(bi-bi_a); end Lp(k)=al3'*H*al3/2+C*sum(abs(e(find(abs(e)>epsi)))-epsi); if(pos<10^-10) hacer=0; nsv=length(i1)+length(i2n)+length(i2p); end end i1p=find(e>=epsi); i1n=find(e<=-epsi); a=zeros(N,1); a(i1p)=C./(e(i1p)-epsi); a(i1n)=-C./(e(i1n)+epsi); a(find(a>K))=K; i2p=find(al3>=(C-C/100) & al3<=(C+C/100) & al3_a>=(C-C/100) & al3_a<=(C+C/100) & e>epsi & 15*(e-epsi)>14*(e_a-epsi)); if(length(setdiff(i1p,i2p))) i1p=setdiff(i1p',i2p)'; else [val,pos]=min(e(i2p)); i2p=setdiff(i2p,i2p(pos)); i1p=setdiff(i1p',i2p)'; end i2n=find(al3>=(-C-C/100) & al3<=(-C+C/100) & al3_a>=(-C-C/100) & al3_a<=(-C+C/100) & e<-epsi & 15*(e+epsi)<14*(e_a+epsi)); if(length(setdiff(i1n,i2n))) i1n=setdiff(