glram.m

算法实现:Jieping Ye. Generalized low rank approximations of matrices. Machine Learning, Vol. 61, pp. 167

function [L,M,R, err]  = GLRAM(A, L, low1, low2, ITE)

%------------------------------------------------------------------
% Input   A: data matrix
%         L: initial L0
%         low1: row dimension of reduced representation M{i}
%         low2: column dimension of reduced representation M{i}
%         ITE: number of iterations
% Output: L: left transformation
%         M: reduced representation
%         R: right transformation
%         err: reconstruction error measured by RMSRE  
%-------------------------------------------------------------------

%[row, col] = size(A{1}); % row and column dimensions of A{i}
n          = size(A,2); % number of data points

%-------------------------------------------------------------------
                                                                                                        
for ite = 1:ITE

MU = 0;
for i =1:n
     TU = L'* A{i};	
     MU = MU + TU'*TU;
end;

[U0,D0,V0] = svd(MU);
R = V0(:,1:low2);

%-------------------------------------------------------------------
 
NU = 0;
for i =1:n
     TV = A{i}*R;
     NU =  NU + TV*TV';
end;

[U1,D1,V1] = svd(NU);
L = V1(:,1:low1);

end;

%-------------------------------------------------------------------

for i =1:n
     M{i} = L'* A{i}*R;
end;


%  Compute the RMSRE value (reconstruction error) 

err =  ERROR(L, M, R, A, n);


%-------------------------------------------------------------------
%                  THE END OF THE MAIN PROGRAM
%-------------------------------------------------------------------      
function error = ERROR(L, M, R, A, n)
%  SUBROUTINE TO COMPUTE THE RMSRE VALUE

error = 0;

for i =1:n
    A_const{i} = L*M{i}*R';
    TEMP       = A{i} - A_const{i};
    error      = error + norm(TEMP,'fro')^2;
end;

error = sqrt(error/n);