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Selecting among three-mode principal component models of different types and complexities: a numerical convex hull
Eva Ceulemans1, Henk A L Kiers
1Katholieke Universiteit Leuven, Belgium. eva.ceulemans@psy.kuleuven.be
Summary
Selecting the best three-mode principal component model for three-way data is crucial. A new convex hull-based heuristic accurately identifies the optimal model and complexity, with minor exceptions for certain Tucker3 data arrays.
Area of Science:
- Multivariate data analysis
- Chemometrics
- Machine learning
Background:
- Three-way, three-mode data analysis requires selecting appropriate principal component models.
- Common models include Candecomp/Parafac, Tucker3, Tucker2, and Tucker1.
Purpose of the Study:
- To propose a numerical model selection heuristic for choosing the best three-mode principal component model.
- To determine the optimal complexity (number of components) for the selected model.
Main Methods:
- Development of a novel model selection heuristic utilizing a convex hull approach.
- Extensive simulations to evaluate the performance of the proposed heuristic.
Main Results:
- The convex hull-based heuristic demonstrates near-perfect performance in model selection.
- Performance is slightly compromised for Tucker3 data arrays with small modes and high error.
Conclusions:
- The proposed heuristic is a reliable tool for selecting appropriate three-mode principal component models.
- It offers a robust method for determining model complexity in multivariate data analysis.
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