The Candecomp/Parafac (CP) model is a well-known tool for summarizing a three-way array by extracting a limited number of components. Unfortunately, in some cases, the model suffers from the so-called degeneracy, that is a solution with diverging and uninterpretable components. To avoid degeneracy, orthogonality constraints are usually applied to one of the component matrices. This solves the problem only from a technical point of view because the existence of orthogonal components underlying the data is not guaranteed. For this purpose, we consider some variants of the CP model where the orthogonality constraints are relaxed either by constraining only a pair, or a subset, of components or by stimulating the CP solution to be possibly orthogonal. We theoretically clarify that only the latter approach, based on the least absolute shrinkage and selection operator and named the CP-Lasso, is helpful in solving the degeneracy problem. The results of the application of CP-Lasso on simulated and real life data show its effectiveness.

Constrained Candecomp/Parafac via the Lasso / Giordani, Paolo; Roberto, Rocci. - In: PSYCHOMETRIKA. - ISSN 0033-3123. - 78:4(2013), pp. 669-684. [10.1007/s11336-013-9321-9]

Constrained Candecomp/Parafac via the Lasso

GIORDANI, Paolo;ROCCI, Roberto
2013

Abstract

The Candecomp/Parafac (CP) model is a well-known tool for summarizing a three-way array by extracting a limited number of components. Unfortunately, in some cases, the model suffers from the so-called degeneracy, that is a solution with diverging and uninterpretable components. To avoid degeneracy, orthogonality constraints are usually applied to one of the component matrices. This solves the problem only from a technical point of view because the existence of orthogonal components underlying the data is not guaranteed. For this purpose, we consider some variants of the CP model where the orthogonality constraints are relaxed either by constraining only a pair, or a subset, of components or by stimulating the CP solution to be possibly orthogonal. We theoretically clarify that only the latter approach, based on the least absolute shrinkage and selection operator and named the CP-Lasso, is helpful in solving the degeneracy problem. The results of the application of CP-Lasso on simulated and real life data show its effectiveness.
2013
orthogonality constraints; candecomp/parafac; degeneracy; lasso
01 Pubblicazione su rivista::01a Articolo in rivista
Constrained Candecomp/Parafac via the Lasso / Giordani, Paolo; Roberto, Rocci. - In: PSYCHOMETRIKA. - ISSN 0033-3123. - 78:4(2013), pp. 669-684. [10.1007/s11336-013-9321-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/491899
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