A weak degeneracy revealing decomposition for the CANDECOMP/PARAFAC model

The CANDECOMP/PARAFAC (CP) model is a well known and frequently used tool for extracting substantial information from a three-way data array. It has several useful characteristics and usually gives meaningful insights about the underlying structure of the data. However, in some cases it has a 'strange' behaviour suffering from the so-called 'degenerate solutions, i.e. solutions where the components show a diverging pattern and are meaningless. Several authors have investigated the causes of degeneracy concluding that the phenomenon is due to a lack of minimum of the loss function. In this paper, we study the degeneracy of CP limiting our attention to the two-component case. The study is done by introducing a canonical form, called 2DR, which is 'weakly degeneracy revealing' On the ground of this framework, degeneracy is studied along with some of the remedies proposed in the literature by using a Tucker3 model having a core in the 2DR form. The analysis gives new insights about the behaviour of the CP model and suggests new ideas on how to deal with degeneracy. Copyright (C) 2010 John Wiley & Sons, Ltd.