Selecting Among Multi-Mode Partitioning Models of Different Complexities: A Comparison of Four Model Selection Criteria

Abstract

Multi-mode partitioning models for N-way N-mode data reduce each of the N modes in the data to a small number of clusters that are mutually exclusive. Given a specific N-mode data set, one may wonder which multi-mode partitioning model (i.e., with which numbers of clusters for each mode) yields the most useful description of this data set and should therefore be selected. In this paper, we address this issue by investigating four possible model selection heuristics: multi-mode extensions of Calinski and Harabasz's (1974) and Kaufman and Rousseeuw's (1990) indices for one-mode k-means clustering and multi-mode partitioning versions of Timmerman and Kiers's (2000) DIFFIT and Ceulemans and Kiers's (2006) numerical convex hull based model selection heuristic for three-mode principal component analysis. The performance of these four heuristics is systematically compared in a simulation study, which shows that the DIFFIT and numerical convex hull heuristics perform satisfactory in the two-mode partitioning case and very good in the threemode partitioning case.