Uni-mode and partial uniqueness conditions for CANDECOMP/PARAFAC of three-way arrays with linearly dependent loadings
type: Item
instance of: scholarly article
zbMATH Open document ID: 1246.15026
DOI: 10.1137/110825765
author: Xijing Guo
author: Sebastian Miron
author: David Brie
author: Alwin Stegeman
published in: SIAM Journal on Matrix Analysis and Applications
publication date: 2012-08-23T00:00:00Z
full work available at URL: 110825765.pdf
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 62H25
zbMATH DE Number: 6070720
zbMATH Keywords: uni-mode uniqueness
zbMATH Keywords: partial uniqueness
zbMATH Keywords: CANDECOMP/PARAFAC
zbMATH Keywords: parallel profiles with linear dependencies
zbMATH Keywords: PARALIND
zbMATH Keywords: constrained factors
zbMATH Keywords: CONFAC
MaRDI profile type: Publication
OpenAlex ID: W2130629120
title: Uni-mode and partial uniqueness conditions for CANDECOMP/PARAFAC of three-way arrays with linearly dependent loadings
review text: Three sufficient conditions are derived for the three-way CANDECOMP/PARAFAC (CP) model, which ensure uniqueness in one of the three modes (``uni-mode-uniqueness''). Based on these conditions, a partial uniqueness condition is proposed which allows collinear loadings in only one mode. It is shown that if there is uniqueness in one mode, then the initial CP model can be uniquely decomposed in a sum of lower-rank tensors for which identifiability can be independently assessed. This condition is simpler and easier to check than other similar conditions existing in the specialized literature. These theoretical results are illustrated by numerical examples.
reviewed by: Andreas Arvanitoyeorgos
description: scientific article; zbMATH DE number 6070720