function alpha=kernelOptimization_c2(trData,ecData,trTags,gamma0,gamma1,epsilon)

% kernel optimization for binary-class data set. The class tags are supposed to be 0, 1.
% "trData": the matrix of the training data.
% "ecData": the matrix of the 'local centers'.
% "trTags": the class tags of the training data.
% "gamma0": the parameter in the basic Gaussian kernel function.
% "gamma1": the parameter in the supplementary Gaussian kernel function.
% "epsilon": the parameter in the disturbed resampling procedure.
% "alpha": the final optimized combination coefficients in out data-dependent kernel model.

iterations=1000;
initialLearningRate=0.01;

trvData=trData;
[trvDim,trvSize]=size(trData);
trbSize=size(ecData,2);

[resData1,resIndex1]=resampling(trvData,trvSize);
[resData2,resIndex2]=resampling(trvData,trvSize);

randn('state',sum(100*clock)); 
trvData1=[trvData,resData1+epsilon*randn(size(trvData)),resData2+epsilon*randn(size(trvData))];
trTags1=[trTags,trTags(resIndex1),trTags(resIndex2)];

[trTags1,nIndex]=sort(trTags1);
trvData1=trvData1(:,nIndex);

kernelMat1=exp(-gamma0*getDistanceMat(trvData1,trvData1));
suppKernelMat1=[ones(size(trvData1,2),1),exp(-gamma1*getDistanceMat(trvData1,ecData))];    

[betweenMat1,withinMat1]=getBasicKernelMat(kernelMat1,trTags1);
bscMat1=suppKernelMat1'*betweenMat1*suppKernelMat1;
bscMat2=suppKernelMat1'*withinMat1*suppKernelMat1;

alpha=zeros(size(ecData,2)+1,1);
alpha(1,1)=1.0;

for i=1:iterations      
   quasi1=suppKernelMat1*alpha;
   J1=quasi1'*betweenMat1*quasi1;
   J2=quasi1'*withinMat1*quasi1;
      
   currentLearningRate=initialLearningRate*(1.0-(i-1)/iterations);
   alpha=alpha+(currentLearningRate/J2/J2)*(J2*bscMat1-J1*bscMat2)*alpha;
   
   alpha=(1.0/sqrt(alpha'*alpha))*alpha;   
end