Selecting among three-mode principal component models of different types and complexities: A numerical convex hull based method

Several three-mode principal component models can be considered for the modelling of three-way, three-mode data, including the Candecomp/Parafac, Tucker3, Tucker2, and Tucker I models. The following question then may be raised: given a specific data set, which of these models should be selected, and at what complexity (i.e. with how many components)? We address this question by proposing a numerical model selection heuristic based on a convex hull. Simulation results show that this heuristic performs almost perfectly, except for Tucker3 data arrays with at least one small mode and a relatively large amount of error.