Some clarifications of remedies for Candecomp/Parafac degeneracy by means of an SVD-penalized approach

The Candecomp/Parafac model is a widely-used tool for synthetizing three-way arrays through a limited number of components. Unfortunately, its applicability may be prevented by the risk of obtaining degenerate solutions, characterized by diverging, highly collinear and uninterpretable components. A recognized remedy is to impose (soft) orthogonality constraints to the components. In this context, a new strategy for solving the degeneracy problem where the orthogonality constraints are suitably relaxed depending on the data is proposed. This allows for a comparative assessment of some existing remedies against degeneracy from both the theoretical and practical point of views.