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- Title
SUFFICIENT CONDITIONS FOR UNIQUENESS IN CANDECOMP/PARAFAC AND INDSCAL WITH RANDOM COMPONENT MATRICES.
- Authors
Stegeman, Alwin; Ten Berge, Jos M. F.; De Lathauwer, Lieven
- 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.
- Subjects
MATHEMATICAL decomposition; MATRICES (Mathematics); TRILINEAR forms; MATHEMATICS; PROBABILITY theory
- Publication
Psychometrika, 2006, Vol 71, Issue 2, p219
- ISSN
0033-3123
- Publication type
Article
- DOI
10.1007/s11336-006-1278-2