Mixture model modal clustering

TL;DR

This paper explores how mixture models can be used for nonparametric modal clustering by identifying clusters as regions around density modes, bridging two major density-based clustering approaches.

Contribution

It introduces two methods to interpret mixture models from a modal clustering perspective, expanding their applicability beyond parametric assumptions.

Findings

Mixture models can be effectively used for nonparametric modal clustering.

Clusters can be defined as domains of attraction of density modes.

Numerical examples demonstrate the practical utility of the proposed methods.

Abstract

The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different mixture components. In modal clustering, clusters are understood as regions of high density separated from each other by zones of lower density, so that they are closely related to certain regions around the density modes. If the true density is indeed in the assumed class of mixture densities, then mixture model clustering allows to scrutinize more subtle situations than modal clustering. However, when mixture modeling is used in a nonparametric way, taking advantage of the denseness of the sieve of mixture densities to approximate any density, then the correspondence between clusters and mixture components may become questionable. In this paper we introduce two methods to adopt a modal clustering point of view after a mixture model fit. Numerous examples are provided to illustrate that mixture modeling can also be used for clustering in a nonparametric sense, as long as clusters are understood as the domains of attraction of the density modes.