Canonical polyadic decomposition of third-order tensors: reduction to generalized eigenvalue decomposition
type: Item
instance of: scholarly article
zbMATH Open document ID: 1306.15022
DOI: 10.1137/130916084
author: Lieven De Lathauwer
author: Ignat Domanov
published in: SIAM Journal on Matrix Analysis and Applications
publication date: 2014-10-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1312.2848
full work available at URL: https://lirias.kuleuven.be/handle/123456789/393094
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 6356190
zbMATH Keywords: canonical polyadic decomposition
zbMATH Keywords: Candecomp/Parafac decomposition
zbMATH Keywords: tensor
zbMATH Keywords: Khatri-Rao product
zbMATH Keywords: compound matrix
zbMATH Keywords: matrix permanent
zbMATH Keywords: mixed discriminant
zbMATH Keywords: algorithm
zbMATH Keywords: eigenvalue decomposition
zbMATH Keywords: matrix pencil
zbMATH Keywords: computational complexity
Wikidata QID: Q60307027
describes a project that uses: PARAFAC
MaRDI profile type: Publication
OpenAlex ID: W1974785908
arXiv ID: 1312.2848
DBLP publication ID: journals/siammax/DomanovL14
title: Canonical polyadic decomposition of third-order tensors: reduction to generalized eigenvalue decomposition
review text: Canonical polyadic decomposition (CPD) of a third-order tensor is the decomposition in a minimal number of rank-1 tensors. The known algebraic algorithms for the computation of the CPD are limited to cases where at least one of the factor matrices has full column rank. A novel approach is presented in this paper which is applicable in cases where none of the factor matrices has full column rank. The procedure is proved for real and exact problems. Whereas the complex numbers could be easily incorporated, the extension for inexact (noisy) problems is only discussed in brief.NEWLINENEWLINETwo algorithms are proposed. Both of them are algebraic in the sense that they rely only on the standard linear algebra operations. Both reduce the problem to the computation of a generalized eigenvalue decomposition of a matrix pencil. They differ by the computational complexity for particular problems.
description: scientific article; zbMATH DE number 6356190