On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
type: Item
instance of: scholarly article
title: On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
zbMATH Open document ID: 1120.15002
author: Alwin Stegeman
author: Nicholas D. Sidiropoulos
published in: Linear Algebra and its Applications
publication date: 2007-01-09T00:00:00Z
review text: The Candecomp/Parafac-decomposition of the real valued three-way array \(X\) is written as \(X=\underline{Y}^{(1)} + \ldots + \underline{Y}^{(R)} +\underline{E}\), where \(\underline{Y}^{(r)}\) are rank one arrays defined as outer products of three specified vectors and \(\underline E\) is a rest term. The question of uniqueness for this decomposition is provided by the theorem of \textit{J. B. Kruskal} [Linear Algebra Appl. 18, 95-138 (1977; Zbl 0364.15021)]. The authors obtain an accessible and more simple proof of Kruskal theorem, which can be easily adopted to the complex case.
reviewed by: Alexander Guterman
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 5083623
zbMATH Keywords: CP-decomposition
zbMATH Keywords: three-way arrays
zbMATH Keywords: Kruskal-rank condition
MaRDI profile type: Publication
full work available at URL: j.laa.2006.08.010
OpenAlex ID: W2008560788
cites work: Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young'' decomposition
cites work: Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints
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cites work: Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
cites work: On uniqueness in CANDECOMP/PARAFAC
DOI: 10.1016/J.LAA.2006.08.010
description: scientific article; zbMATH DE number 5083623