On the Non-Existence of Optimal Solutions and the Occurrence of "Degeneracy" in the CANDECOMP/PARAFAC Model

Autor/inn/en	Krijnen, Wim P.; Dijkstra, Theo K.; Stegeman, Alwin
Titel	On the Non-Existence of Optimal Solutions and the Occurrence of "Degeneracy" in the CANDECOMP/PARAFAC Model
Quelle	In: Psychometrika, 73 (2008) 3, S.431-439 (9 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0033-3123
DOI	10.1007/s11336-008-9056-1
Schlagwörter	Factor Analysis; Models; Matrices + Suchen Sie Ihr Suchwort? Faktorenanalyse; Analogiemodell; Matrizenrechnung
Abstract	The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of "R" factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence of CP factors monotonically decreasing the CP criterion value to its infimum will exhibit the features of a so-called "degeneracy". That is, the parameter matrices become nearly rank deficient and the Euclidean norm of some factors tends to infinity. We also show that the CP criterion function does attain its infimum if one of the parameter matrices is constrained to be column-wise orthonormal. (As Provided).
Anmerkungen	Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10