title: Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices.
abstract: A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. We examine the uniqueness of the Candecomp/Parafac and Indscal decompositions. In the latter, the array to be decomposed has symmetric slices. We consider the case where two component matrices are randomly sampled from a continuous distribution, and the third component matrix has full column rank. In this context, we obtain almost sure sufficient uniqueness conditions for the Candecomp/Parafac and Indscal models separately, involving only the order of the three-way array and the number of components in the decomposition. Both uniqueness conditions are closer to necessity than the classical uniqueness condition by Kruskal.
authors.affiliation: University of Groningen, Groningen. a.w.stegeman@rug.nl.|Heijmans Institute of Psychological Research, University of Groningen, Grote Kruisstraat 2/1, 9712 TS, Groningen, The Netherlands. a.w.stegeman@rug.nl.
authors.forename: Alwin
authors.initials: A
authors.lastname: Stegeman
authors.affiliation: University of Groningen, Groningen.
authors.forename: Jos M F Ten
authors.initials: JM
authors.lastname: Berge
authors.affiliation: ETIS, UMR 8051, Cergy-Pontoise.
authors.forename: Lieven De
authors.initials: L
authors.lastname: Lathauwer
keywords: Candecomp; Indscal; Parafac; three-way arrays; uniqueness