gradwbfixed.m

用于matlab环境下的支持向量机svm的工具箱

function [grad] = gradwbfixed(Sigma,indsup,Alpsup,w0,C,Xapp,yapp,Sigmaold,pow);
%GRADWBFIXED Computes the gradient of an upper bound on SVM loss wrt SIGMA^POW  
%  GRAD = GRADWBFIXED(SIGMA,INDSUP,ALPSUP,W0,C,XAPP,YAPP,SIGMAOLD,POW) 
%  is the gradient of the upper bound on the SVM loss obtained when the 
%  weight and bias parameters are considered to be unaffected by SIGMA. 
%  
%  SIGMA is the current SIGMA value
%  INDSUP is the (nsup,1) index of current support vectors 
%  ALPSUP is the (nsup,1) vector of non-zero Lagrange multipliers
%  W0 is the bias parameter
%  C is the error penalty hyper-aparameter
%  XAPP,YAPP are the learning examples
%  SIGMAOLD is the SIGMA value corresponding to the current weights

%  27/01/03 Y. Grandvalet

% initialization

nsup  = length(indsup);
[n,d] = size(Xapp);

% I) compute slack variables, old Sigma on support, new sigma on data points

% I.1)  distances

XsupS0 = Xapp(indsup,:).*repmat(Sigmaold,nsup,1);
XappS = Xapp.*repmat(Sigma,n,1);
Dist  = XsupS0*XappS';
Dist  = Dist - repmat(0.5*sum(XsupS0.^2,2),1,n) - repmat(0.5*sum(XappS.^2,2)',nsup,1) ; % - 1/2 ||Sigma . xi - Sigmaold . xj||^2
Dist  = exp(Dist) ;

% I.2) slacks

xi = 1 - yapp.*((Dist'*Alpsup) + w0); 

% II) end: gradient

ind = find(xi>=0) ;

grad = zeros(1,d);
for k=1:d;
   Distk   = repmat(XappS(ind,k)',nsup,1) - repmat(XsupS0(:,k),1,length(ind)) ;
   grad(k) =  Alpsup' * (Distk.*Dist(:,ind)) * (Xapp(ind,k).*yapp(ind)) ;
end;

ind = find(Sigma~=0);
grad(ind) = C*grad(ind).*(1/pow*abs(real(Sigma(ind).^(1-pow))));