bh_ClassHSIC_ObjTerm.m

function [KH,LH] = bh_ClassHSIC_ObjTerm(Data,label)
%%
% this function computes the objective term for the HSIC-LASSO feature selection model
   % -- Data  --training data samples of the form nsamples x nfeatures
   % -- label  -- corresponding label of the training samples
   
  % Output
     % KH  -- is the design matrix in the feature selection model
     % LH  -- is the target matrix in the feature selection model

%%
globalsigma = 0
dimension_wise_sigma=1
%
[n,d] = size(Data);
Nclass=length(unique(label));

if globalsigma
    sigma=compmedDist(Data);
    sigma= sigma^2;
end


%H = eye(Nclass) - 1/Nclass*ones(Nclass); % centeralizing matrix
H=eye(Nclass);
KH=zeros(Nclass*Nclass,d);
for loop=1:d
    KS=cell(Nclass,Nclass);HSICM=zeros(Nclass,Nclass);
    K=cell(Nclass,1);
    if dimension_wise_sigma
        sigma=compmedDist(Data(:,loop));
        sigma=sigma^2;
        if isnan(sigma)
            sigma = 4.27e-16;
        end
    end
    for i=1:Nclass
        i_index=(label==i);

        [K{i}]=bh_rbf(Data(i_index,loop),sigma);
        for j=1:Nclass
            j_index=(label==j);
 
            [KS{i,j}]=bh_surrogatekernel(Data(i_index,loop),Data(j_index,loop),sigma);

            % HSIC measure
            HSICM(i,j)=bh_HSIC(KS{i,j},K{i});
            
        end
        
    end

    tmp=HSICM; 

    tmp=H*tmp*H;
 
     
    KH(:,loop)=tmp(:);
end

  I=(1/Nclass)*eye(Nclass);   % target matrix
  %I=eye(Nclass);              % target matrix
  I=H*I*H;
  
  LH=I(:);