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ERIC Number: EJ812124
Record Type: Journal
Publication Date: 2008-Sep
Pages: 9
Abstractor: As Provided
Reference Count: 0
ISSN: ISSN-0033-3123
On the Non-Existence of Optimal Solutions and the Occurrence of "Degeneracy" in the CANDECOMP/PARAFAC Model
Krijnen, Wim P.; Dijkstra, Theo K.; Stegeman, Alwin
Psychometrika, v73 n3 p431-439 Sep 2008
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.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A