, Volume 71, Issue 2, pp 219–229 | Cite as

Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices

  • Alwin Stegeman
  • Jos M. F. Ten Berge
  • Lieven De Lathauwer


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.


Candecomp Parafac Indscal three-way arrays uniqueness 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Alwin Stegeman
    • 1
    • 3
  • Jos M. F. Ten Berge
    • 1
  • Lieven De Lathauwer
    • 2
  1. 1.University of GroningenGroningen
  2. 2.ETISUMR 8051
  3. 3.Heijmans Institute of Psychological ResearchUniversity of GroningenGroningenThe Netherlands

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