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brede_mat_reconerror

PURPOSE ^

brede_mat_reconerror - Reconstruction error for a matrix

SYNOPSIS ^

function RE = brede_mat_reconerror(X, L, M, R, varargin)

DESCRIPTION ^

 brede_mat_reconerror - Reconstruction error for a matrix

       E = brede_mat_reconerror(X, L, M, R)
       E = brede_mat_reconerror(X, L, R)

       Input:    X     Original matrix as a 'mat' structure
                 L     Left matrix as a 'mat' structure
                 M     Middle matrix as a 'mat' structure
                 R     Right matrix as a 'mat' structure

       Property: Subspaces   [ {1:size(M.matrix,1)} | nonnegative
                       integers ] The subspaces the reconstruction
                       error is computed in. 

       Output:   RE    Reconstruction error as a vector

       Computes a reconstruction error, that is the difference
       between an 'original' matrix X and the product of its
       decomposed matrices L*M*R (or L*R).   

          U = X - L*M*R      or    U = X - L*R
 
       The reconstruction error is computed as the Frobenius norm, ie,
       the trace of the square error matrix trace(U'*U)
 
          RE = norm(U, 'fro')^2

       The reconstruction error is by default computed for subspace
       from 1 to the size of the decomposed subspace and returned as
       a vector with the first element being the reconstruction error
       for a subspace with dimension one using the first column in L
       and first row in R.
         
       See also BREDE, BREDE_MAT, BREDE_MAT_NMF, BREDE_MAT_SVD.

 $Id: brede_mat_reconerror.m,v 1.4 2004/10/14 17:03:55 fnielsen Exp $

CROSS-REFERENCE INFORMATION ^

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