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Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
Alwin Stegeman1,2, Jos M F Ten Berge3, Lieven De Lathauwer4
1University of Groningen, Groningen. a.w.stegeman@rug.nl.
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.
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