A Counterexample to the Possibility of an Extension of the Eckart-Young Low-rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition

Abstract

Earlier work has shown that no extension of the Eckart–Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart–Young SVD approximation theorem to the orthogonal rank tensor decomposition, answering an open question previously posed by Kolda [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 243–355].

Type
Journal
Publication
SIAM Journal on Matrix Analysis and Applications
Date
Tags
Tensors
Links
PDF DOI
Citation
T. G. Kolda. A Counterexample to the Possibility of an Extension of the Eckart-Young Low-rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition. SIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 3, pp. 762-767, 2003. https://doi.org/10.1137/S0895479801394465

Keywords

singular value decomposition, principal components analysis, multidimensional arrays, higher-order tensor, multilinear algebra

BibTeX

@article{Ko03,  
author = {Tamara G. Kolda}, 
title = {A Counterexample to the Possibility of an Extension of the {Eckart-Young} Low-rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition}, 
journal = {SIAM Journal on Matrix Analysis and Applications}, 
volume = {24}, 
number = {3}, 
pages = {762--767}, 
month = {January}, 
year = {2003},
doi = {10.1137/S0895479801394465},
}