lshssvmtrain.m

Matlab codes for Hidden Sapce Support vector machines

function [alpha,bias, svi, nsv] = lshsvmtrain(samplesX,samplesY,kernel,kernelparam,C,threshold,percent)


  if (nargin ~=7) % check correct number of arguments
    help svc
  else

    fprintf('Least Square Hidden Space Support Vector Machines\n')
    fprintf('__________________________________________________\n')
    n = size(samplesX,1);
   
    % Construct the Kernel matrix
    fprintf('Constructing ...\n');
    K = zeros(n,n);  
    st = cputime;
    for i=1:n
          K(:,i) = bsvkernel(samplesX,samplesX(i*ones(n,1),:),kernel,kernelparam);
    end
   
    % Solve the Optimisation Problem
    fprintf('Optimising ...\n');
    if threshold
        H = [(K'*K)+eye(size(K))/2/C K*ones(n,1); ones(1,n)*K  n]; 
        c = -[K*samplesY; samplesY'*ones(n,1)];
        R = inv(H);
        alpha = R*(-c);
        svi = 1:n;
        error = percent*(-c'*(alpha));
        perror = 0;
        for i=1:n
            tempR               = diag(R);
            tempR(end)          = [];
            [temp,i_out]        = min(alpha(svi).^2./tempR);
            perror = perror + temp;
            if perror > error
                break;
            end
            tempsvi             = [svi,n+1];
            alpha(tempsvi)      = alpha(tempsvi) - alpha(svi(i_out))*R(:,i_out)/R(i_out,i_out);
            svi(i_out)          = [];
            R                   = removeone(R,i_out);
        end
        nsv = length(svi);
        bias = alpha(end);
        alpha = alpha(1:n);
    else
        H = (K'*K)+eye(size(K))/2/C; 
        c = -K*samplesY;
        R = inv(H);
        alpha = R*(-c);
        bias = 0;
        error = percent*(-c'*(alpha));
        perror = 0;
        svi = 1:n;
        for i=1:n
            tempR               = diag(R);
            [temp,i_out]        = min(alpha(svi).^2./tempR);
            perror = perror + temp;
            if perror > error
                break;
            end
            alpha(svi)      = alpha(svi) - alpha(svi(i_out))*R(:,i_out)/R(i_out,i_out);
            svi(i_out)          = [];
            R                   = removeone(R,i_out);
        end
        nsv = length(svi);
    end
%     KK = K(:,svi);
%     [U,S] = svd(KK);
%     nn = 13;
%     lamdavec = 2.^linspace(0,-12,nn);
%         for i = 1:nn
%             lamda = lamdavec(i); 
%             diagD = diag(S.^2)./diag(S.^2 + lamda);
%             diagD = [diagD; zeros(n-nsv,1)];
%             switch 'cv'
%             case 'cv'
%                 Tr = 1 - sum(U.*(ones(n,1)*diagD').*U,2);            
%                 Error = samplesY - U*(diagD.*(U'*samplesY));
%                 loovec(i) = mean((Error./Tr).^2);
%             case 'gcv'
%                 Error = samplesY - U*(diagD.*(U'*samplesY));
%                 p = sum(diagD)/n;
%                 loovec(k,i) = mean(Error.^2)/(1-p).^2;
%             case 'aic'
%                 Error = samplesY - U*(diagD.*(U'*samplesY));
%                 p = sum(diagD)/n;
%                 loovec(k,i) = mean(Error.^2)*(1+p)/(1-p);
%             case 'bic'
%                 Error = samplesY - U*(diagD.*(U'*samplesY));
%                 p = sum(diagD)/n;
%                 loovec(k,i) = mean(Error.^2)*(1+log(n)/2*p/(1-p));
%             case 'sms'
%                 Error = samplesY - U*(diagD.*(U'*samplesY));
%                 p = sum(diagD)/n;
%                 loovec(k,i) = mean(Error.^2)*(1+2*p);
%             case 'vm'
%                 Error = samplesY - U*(diagD.*(U'*samplesY));
%                 p = (sum(diagD))/n;
%                 factor = 1;
%                 loovec(k,i) = mean(Error.^2)/(1-factor*sqrt(p-p*log(p)+log(n)/2/n));
%             end
%         end
%     fprintf('Execution time : %4.1f seconds\n',cputime - st);    
%     [looe,index1] = min(loovec);
%     lamda = lamdavec(index1);
%     alpha(svi) = (KK'*KK + lamda*eye(nsv,nsv))\(KK'*samplesY);

    fprintf('Execution time: %4.1f seconds\n',cputime - st);  
end