irwls_pd_svr_nobias

PURPOSE ^

ADAPTIVE SVR USING IRWLS WITH NO BIAS.

SYNOPSIS ^

function [nsv,al3,bi]=irwls_pd_svr_nobias(x,y,H,C,D,epsi,F);

DESCRIPTION ^

    ADAPTIVE SVR USING IRWLS WITH NO BIAS.
    VERSION 2: SOLVE ONLY THE MINIMIZATION WRT W

  [nsv,al3,bi]=irwls(x,y,ker,C,tol,epsi);

  Input parameters:
       x: input vectors.
       y: output samples for x.
       H: kernel matrix.
       C: Penalization constraint.
        D: C profile
       epsi: insensitivity zone.
        F: epsilon profile

  Output parameters:
        nsv: number of support vectors
        al3: dual weights
        bi: bias term

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 
0002 %
0003 %    ADAPTIVE SVR USING IRWLS WITH NO BIAS.
0004 %    VERSION 2: SOLVE ONLY THE MINIMIZATION WRT W
0005 %
0006 %  [nsv,al3,bi]=irwls(x,y,ker,C,tol,epsi);
0007 %
0008 %  Input parameters:
0009 %       x: input vectors.
0010 %       y: output samples for x.
0011 %       H: kernel matrix.
0012 %       C: Penalization constraint.
0013 %        D: C profile
0014 %       epsi: insensitivity zone.
0015 %        F: epsilon profile
0016 %
0017 %  Output parameters:
0018 %        nsv: number of support vectors
0019 %        al3: dual weights
0020 %        bi: bias term
0021 
0022 function [nsv,al3,bi]=irwls_pd_svr_nobias(x,y,H,C,D,epsi,F);
0023 
0024 T=clock;
0025 if (nargin<7 | nargin>7)
0026     help irwls_adapta_nobias2
0027 else
0028 
0029     tol=10^-4;
0030     K=10^8;
0031     val_a=100;
0032     N=length(x);
0033     ns=-1;
0034     k=1;
0035     hacer=1;
0036     bi=0;
0037 
0038     i1p=1:2:N;
0039     i1n=2:2:N;
0040     i1=[i1p i1n];
0041 
0042     epsi = epsi./F;
0043 
0044     a(i1)=C*D(i1);
0045     al3=zeros(N,1);
0046     bi=0;
0047     i2p=[];
0048     i2n=[];
0049     e=y;
0050 
0051     while(hacer)
0052         al3_a=al3;
0053         bi_a=bi;
0054         al3=zeros(N,1);
0055         al3(i2p)=C*D(i2p);
0056         al3(i2n)=-C*D(i2n);
0057 
0058         if(length(i1))
0059 
0060             Xi=inv(H(i1,i1)+diag(1./(a(i1))));
0061             E=ones(N,1);
0062             E(i1n)=-1;
0063 
0064             if (length(i2n)==0) & (length(i2p)==0)
0065                 aux=Xi*(y(i1)-E(i1).*epsi(i1));
0066             elseif (length(i2n)==0) & (length(i2p)~=0)
0067                 aux=Xi*(y(i1)-E(i1).*epsi(i1)-C*H(i1,i2p)*D(i2p));
0068             elseif (length(i2n)~=0) & (length(i2p)==0)
0069                 aux=Xi*(y(i1)-E(i1).*epsi(i1)+C*H(i1,i2n)*D(i2n));
0070             else
0071                 aux=Xi*(y(i1)-E(i1).*epsi(i1)+C*H(i1,i2n)*D(i2n)-C*H(i1,i2p)*D(i2p));
0072             end;
0073 
0074             al3(i1)=aux(1:length(i1));
0075 
0076             bi=0;
0077         end
0078 
0079         e_a=e;
0080 
0081         I=find(al3-al3_a);
0082         if(length(I))
0083             e=e_a-H(:,I)*(al3(I)-al3_a(I));
0084         end
0085 
0086         if((max(abs(e-e_a))<tol & k>(ns+1)) | k>=2000)
0087             nsv=length(i1)+length(i2n)+length(i2p);
0088             hacer=0;
0089         else
0090 
0091             i1p=find(e>epsi);
0092             i1n=find(e<-epsi);
0093             i2p=find(e>epsi & al3==C*D);
0094             i2n=find(e<-epsi & al3==-C*D);
0095 
0096             a=zeros(N,1);
0097             a(i1p)=C*D(i1p)./(e(i1p)-epsi(i1p));
0098             a(i1n)=-C*D(i1n)./(e(i1n)+epsi(i1n));
0099             a(find(a>K))=K;
0100 
0101             i2p_c=find(al3>=(C*D-C*D/100) & al3<=(C*D+C*D/100) & e>epsi & a<val_a);
0102             i2p_c=setdiff(i2p_c',i2p)';
0103             i2p=sort([i2p' i2p_c'])';
0104             i1p=setdiff(i1p',i2p)';
0105 
0106             i2n_c=find(al3>=(-C*D-C*D/100) & al3<=(-C*D+C*D/100) & e<-epsi & a<val_a);
0107             i2n_c=setdiff(i2n_c',i2n)';
0108             i2n=sort([i2n' i2n_c'])';
0109             i1n=setdiff(i1n',i2n)';
0110 
0111             i1=[i1p;i1n];
0112 
0113             if(length(i1)==0)
0114                 [val,pos]=min(e(i2p));
0115                 i1p=i2p(pos);
0116                 i2p=setdiff(i2p',i1p)';
0117                 a(i1p)=C*D(i1p)./(e(i1p)-epsi(i1p));
0118 
0119                 [val,pos]=max(e(i2n));
0120                 i1n=i2n(pos);
0121                 i2n=setdiff(i2n',i1n)';
0122                 a(i1n)=C*D(i1n)./(e(i1n)-epsi(i1n));
0123             end
0124 
0125             k=k+1;
0126             if(rem(k,20)==0 & max(abs(e-e_a))<(tol*10))
0127                 val_a=min(val_a*2,1000);
0128             end
0129         end
0130     end
0131 end

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