On uniqueness in CANDECOMP/PARAFAC

Psychometrika

Volumn 67, Issue 3, 2002, Pages 399-409

  Ten Berge, Jos M F ^a   Sidiropoulos, Nikolaos D ^b  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Candecomp; Parafac; Three way arrays; Uniqueness

Indexed keywords

EID: 0036746455     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02294992     Document Type: Article

References (9)

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2. Harshman, R.L. (1970). Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multimodal factor analysis. UCLA Working Papers in Phonetics, 16, 1-84. (http://publish.uwo.ca/∼harshman/)
3. Harshman, R.L. (1972). Determination and proof of minimum uniqueness conditions for PARAFACl. UCLA Working Papers in Phonetics, 22, 111-117. (http://publish.uwo.ca/∼harshman/)
4. Krijnen, W.P. (1993). The analysis of three-way arrays by constrained PARAFAC methods. Leiden, Netherlands: DSWO Press.
5. Kruskal, J.B. (1977). Three-way arrays: Rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics. Linear Algebra and Its Applications, 18, 95-138.
6. Kruskal, J.B. (1989). Rank, decomposition, and uniqueness for 3-way and N-way arrays. In R. Coppi & S. Bolasco (Eds.), Multiway data analysis (pp. 7-18). Amsterdam, Netherlands: North-Holland.
7. Liu, X., & Sidiropoulos, N.D. (2001). Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays. IEEE Transactions on Signal Processing, 49, 2074-2086.
8. Paatero, P. (1999). The multilinear engine - A table-driven least squares program for solving multilinear programs, including the n-way parallel factor analysis model. Journal of Computational and Graphical Statistics, 8, 854-888.
9. Sidiropoulos, N.D., & Bro, R. (2000). On the uniqueness of multilinear decomposition of N-way arrays. Journal of Chemometrics, 14, 229-239.