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Constrained Candecomp/Parafac via the Lasso

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  • Paolo Giordani
  • Roberto Rocci

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. Copyright The Psychometric Society 2013

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  • Paolo Giordani & Roberto Rocci, 2013. "Constrained Candecomp/Parafac via the Lasso," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 669-684, October.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:4:p:669-684
    DOI: 10.1007/s11336-013-9321-9
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    References listed on IDEAS

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    1. Wim Krijnen & Theo Dijkstra & Alwin Stegeman, 2008. "On the Non-Existence of Optimal Solutions and the Occurrence of “Degeneracy” in the CANDECOMP/PARAFAC Model," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 431-439, September.
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