Dipartimento di Scienze Statistiche

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 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 theoretical 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 clarify theoretically that only the latter approach, based on the Least absolute shrinkage and selection operator (Lasso), is effective for solving the degeneracy problem. The results of two applications to real life data show its usefulness in practice.