Information criterion-based non-hierarchical clustering

Abstract

In the analysis of actual data, it is important to determine whether there are clusters in the data. This can be done using one of several methods of cluster analysis, which can be roughly divided into hierarchical and nonhierarchical clustering methods. Nonhierarchical clustering can be applied to more types of data than can hierarchical clustering (see e.g., Saito and Yadohisa, 2006), and hence, in this paper, we focus on nonhierarchical clustering. In nonhierarchical clustering, the results heavily depend on the number of clusters, and thus it is very important to select the appropriate number of clusters. Bozdogan (1986) and Manning et al. (2009, Section 16.4.1) used formal information criteria, e.g., Aakaike's information criterion (AIC) and so on, for selecting the number of clusters. In this paper, we verify that such formal information criteria work poorly for selecting the number of clusters by conducting numerical examinations. Hence, we extend a formal AIC by adding a new penalty term, and search for an additional penalty with an acceptable selection-performance through numerical experiments.