Quantifying Distances Between Clusters with Elliptical or Non-Elliptical Shapes

TL;DR

This paper introduces measures for quantifying distances between clusters with various shapes, including non-elliptical, to improve interpretation and comparison of complex clustering models in health data.

Contribution

It proposes practical measures and computational tools for assessing multivariate distances between diverse cluster shapes, validated through simulations and real health data.

Findings

Measures effectively distinguish clusters with different means, scales, and rotations.

Simulation results demonstrate robustness of the measures across scenarios.

Application to health data illustrates practical utility in real-world clustering.

Abstract

Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data, rather than forcing a series of elliptical clusters. These methods are highly relevant for clustering continuous non-normal data - a common occurrence with objective data that are now routinely captured in health research. However, interpreting and comparing such models - especially with regards to whether they produce meaningful clusters that are reasonably well separated - is non-trivial. We summarize several measures that can succinctly quantify the multivariate distance between two clusters, regardless of the cluster distribution, and suggest practical computational tools. Through a simulation study, we evaluate these measures across three scenarios that allow for clusters to differ in mean, scale, and rotation. We then demonstrate our approaches using physiological responses to emotional imagery captured as part of the Transdiagnostic Anxiety Study, a large-scale study of anxiety disorder spectrum patients and control participants. Finally, we synthesize findings to provide guidance on how to use distance measures in clustering applications.