A concise proof of Kruskal's theorem on tensor decomposition

Linear Algebra and Its Applications

Volumn 432, Issue 7, 2010, Pages 1818-1824

  Rhodes, John A ^a  

^a UNIVERSITY OF ALASKA FAIRBANKS   (United States)

Author keywords

Candecomp; Parafac; Tensor rank

Indexed keywords

CANDECOMP; KRUSKAL; PARAFAC; STATISTICAL MODELS; TENSOR DECOMPOSITION; THIRD-ORDER TENSORS;

THEOREM PROVING;

TENSORS;

EID: 74449089484     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2009.11.033     Document Type: Article

References (14)

1. Allman E.S., Matias C., and Rhodes J.A. Identifiability of parameters in latent structure models with many observed variables. Ann. Statist. 37 6A (2009) 3099-3132
2. Allman E.S., and Rhodes J.A. The identifiability of covarion models in phylogenetics. IEEE/ACM Trans. Comput. Biol. Bioinformatics 6 (2009) 76-88
3. Anderson T.W. On estimation of parameters in latent structure analysis. Psychometrika 19 (1954) 1-10 (MR MR0075492 (17,756e))
4. Chang J.T. Full reconstruction of Markov models on evolutionary trees: identifiability and consistency. Math. Biosci. 137 1 (1996) 51-73 (MR 97k:92011)
5. Comon P., ten Berge J.M.F., De Lathauwer L., and Castaing J. Generic and typical ranks of multi-way arrays. Linear Algebra Appl. 430 11-12 (2009) 2997-3007 (MR MR2517853)
6. De Lathauwer L. A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalizations. SIAM J. Matrix Anal. Appl. 28 3 (2006) 642-666
7. De Lathauwer L., De Moor B., and Vandewalle J. Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition. SIAM J. Matrix Anal. Appl. 26 2 (2004) 295-327
8. Jiang T., and Sidiropoulos N.D. Kruskal's permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints. IEEE Trans. Signal Process. 52 9 (2004) 2625-2636
9. Kruskal J.B. Rank, decomposition, and uniqueness for 3-way and N-way arrays. Multiway Data Analysis (Rome, 1988) (1989), North-Holland, Amsterdam pp. 7-18 (MR MR1088949)
10. Kruskal J.B. More factors than subjects, tests and treatments: an indeterminacy theorem for canonical decomposition and individual differences scaling. Psychometrika 41 3 (1976) 281-293 (MR MR0488592 (58 #8119))
11. Kruskal J.B. Three-way arrays: rank and uniqueness of trilinear decompositions with application to arithmetic complexity and statistics. Linear Algebra Appl. 18 2 (1977) 95-138 (MR MR0444690 (56 #3040))
12. J.M. Landsberg, Kruskal's theorem, 2009, preprint, arXiv:0902.0543.
13. Stegeman A., and Sidiropoulos N.D. On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition. Linear Algebra Appl. 420 (2007) 540-552
14. Stegeman A., ten Berge J.M.F., and De Lathauwer L. Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices. Psychometrika 71 (2006) 219-229