function [rate, maroc, sigma, gama, c, pred, model]=svm_manifold_aucsort(com,label,list)

%get the number of subjects
  [n,m,v]=size(com);

%get the number of components of each individual
  m=length(list);

ncom=zeros(n,v,m);
% normalizing
 for i=1:n
  if(m==1)
    tmp=(squeeze(com(i,list,:)));
    ncom(i,:)=tmp*(tmp'*tmp)^(-1/2);
  else
    tmp=(squeeze(com(i,list,:)))';
    ncom(i,:,:)=tmp*(tmp'*tmp)^(-1/2);
  end
 end

%using projection matric to compute the distance
dist=zeros(n)+eye(n);
for i=1:n-1
  for j=i:n
     if(i<j)
       if(m==1)
         s=svd(ncom(i,:)*ncom(j,:)');
       else
         s=svd(squeeze(ncom(i,:,:))'*squeeze(ncom(j,:,:)));
       end
       dist(i,j)=sum(s(:).^2)/m;
       %dist(i,j)=real(sqrt(sum(s(:).^2)/m));
       %dist(i,j)=real(sqrt(m-sum(s(:).^2)));
       dist(j,i)=dist(i,j);
       
     end
   end
end

cc=[1 10 100];

sigm_set=0;%sigmamin:.2:sigmamax;
gama_set=1;

label=label(:);
% svm based classification

for g=1:length(gama_set)
    gama=gama_set(g);    
for i=1:length(sigm_set)
  
  sigm=sigm_set(i);
  kernel_=tanh(sigm+gama.*dist);
  
  for j=1:length(cc)
    for k=1:n
      train_list=[1:k-1 k+1:n]';
      test_list=k;
     
       model_precomputed = svmtrain(label(train_list), [train_list, kernel_(train_list,:)], sprintf('-q -b 1 -t 4 -c %f',cc(j)));
       [predict_label_P(k), accuracy_P, tdec_values_P] = svmpredict(label(test_list), [k, kernel_(test_list,:)], model_precomputed,'-b 1');
      %}
       [tmp,idx]=max(tdec_values_P);
       %dec_values_P(k)= tdec_values_P*model_precomputed.Label;
       dec_values_P(k)= tmp*model_precomputed.Label(idx);
      % clear tdec_values_P tmp idx train_list test_list model_precomputed;
    end
    cor(g,i,j)=length(find((label(:)-predict_label_P(:))==0))/n;
    [tp,fp]=roc(label(:),dec_values_P(:));
    aroc(g,i,j)=auroc(tp,fp);%figure;plot(fp,tp); sigm(i), cc(j), cor(i,j)
  end
end 
end
% use AUC to selecte the best performance
iidx=find(aroc==max(aroc(:)));
[q,u,v]=ind2sub(size(aroc),iidx);
tmpcor=cor(find(aroc==max(aroc(:))));

w=find(tmpcor==max(tmpcor(:)));
q=q(w(1));
u=u(w(1));
v=v(w(1));
rate=max(tmpcor(:));

maroc=max(aroc(:));
c=cc(v);
sigma=sigm_set(u);
gama=gama_set(q);
kernel_=tanh(sigma+gama.*dist);
for i=1:n
  train_list=[1:i-1 i+1:n]';
  test_list=i;
  model{i} = svmtrain(label(train_list), [train_list, kernel_(train_list,:)], sprintf('-q -t 4 -c %f -b 1',c));
  [pred(i), accuracy_P, dec_values_P] = svmpredict(label(test_list), [i, kernel_(test_list,:)], model{i},'-b 1');

end