Mixture Complexity and Its Application to Gradual Clustering Change Detection

TL;DR

This paper introduces mixture complexity (MC), a new information-theoretic measure for assessing cluster size in mixture models, enabling detection of gradual clustering changes and analysis of hierarchical substructures.

Contribution

It proposes a novel continuous measure called mixture complexity (MC) for better cluster size estimation in mixture models, especially under overlaps and biases, and applies it to gradual clustering change detection.

Findings

MC allows earlier detection of clustering changes.

MC can distinguish significant from insignificant changes.

Decomposition of MC reveals hierarchical substructures.

Abstract

In model-based clustering using finite mixture models, it is a significant challenge to determine the number of clusters (cluster size). It used to be equal to the number of mixture components (mixture size); however, this may not be valid in the presence of overlaps or weight biases. In this study, we propose to continuously measure the cluster size in a mixture model by a new concept called mixture complexity (MC). It is formally defined from the viewpoint of information theory and can be seen as a natural extension of the cluster size considering overlap and weight bias. Subsequently, we apply MC to the issue of gradual clustering change detection. Conventionally, clustering changes has been considered to be abrupt, induced by the changes in the mixture size or cluster size. Meanwhile, we consider the clustering changes to be gradual in terms of MC; it has the benefits of finding the changes earlier and discerning the significant and insignificant changes. We further demonstrate that the MC can be decomposed according to the hierarchical structures of the mixture models; it helps us to analyze the detail of substructures.