The Carroll and Chang conjecture of equal Indscal components when Candecomp/Parafac gives perfect fit

Linear Algebra and Its Applications

Volumn 430, Issue 2-3, 2009, Pages 818-829

  Ten Berge, Jos M F ^a   Stegeman, Alwin ^a   Bennani Dosse, Mohammed ^b  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b UNIVERSITÉ RENNES 2   (France)

Author keywords

Candecomp; Equivalence; Indscal; k Rank; Parafac; Three way arrays; Typical rank

Indexed keywords

EID: 55549090669     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.09.023     Document Type: Article

References (9)

1. Bennani Dosse M., and Ten Berge J.M.F. The assumption of proportional components when Candecomp is applied to symmetric matrices in the context of Indscal. Psychometrika 73 (2008) 303-307
2. Carroll J.D., and Chang J.J. Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition. Psychometrika 35 (1970) 283-319
3. R.A. Harshman, Foundations of the PARAFAC procedure: models and conditions for an "explanatory" multi-modal factor analysis, UCLA Working Papers in Phonetics, vol. 16, 1970, pp. 1-84.
4. Kruskal J.B. Three-way arrays: rank and uniqueness of trilinear decompositions with applications to arithmetic complexity and statistics. Linear Algebra Appl. 18 (1977) 95-138
5. Rocci R., and Ten Berge J.M.F. A simplification of a result by Zellini on the maximal rank of a symmetric three-way array. Psychometrika 59 (1994) 377-380
6. Rocci R., and Ten Berge J.M.F. Transforming three-way arrays to maximal simplicity. Psychometrika 67 (2002) 351-365
7. Ten Berge J.M.F., and Kiers H.A.L. Some clarifications of the CANDECOMP algorithm applied to Indscal. Psychometrika 56 (1991) 317-326
8. Ten Berge J.M.F., Sidiropoulos N.D., and Rocci R. Typical rank and Indscal dimensionality for symmetric arrays of order I × 2 × 2 or I × 3 × 3. Linear Algebra Appl. 388 (2004) 363-377
9. J.N. Tendeiro, J.M.F. Ten Berge, H.A.L. Kiers, Simplicity transformations for three-way arrays with symmetric slices, and applications to Tucker-3 models with sparse core arrays. Linear Algebra Appl., in press.