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

Ceulemans Eva. | Zendy; Kiers Henk A. L. | Zendy

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

Author(s) -

Ceulemans Eva.,

Kiers Henk A. L.

Publication year - 2006

Publication title -

british journal of mathematical and statistical psychology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.157

H-Index - 51

eISSN - 2044-8317

pISSN - 0007-1102

DOI - 10.1348/000711005x64817

Subject(s) - convex hull , principal component analysis , heuristic , mode (computer interface) , hull , set (abstract data type) , component (thermodynamics) , regular polygon , computer science , convex combination , model selection , algorithm , data set , mathematics , mathematical optimization , convex optimization , artificial intelligence , engineering , geometry , physics , marine engineering , thermodynamics , programming language , operating system

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 Tucker1 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.

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