Model--based clustering for spherical and hyper--spherical data using elliptically symmetric distributions

2026-05-26

AI Summary

This study addresses the limitations of traditional clustering methods for spherical and hyperspherical data, which often rely on rotationally symmetric distributions and struggle to capture complex structures. To overcome this constraint, the authors propose a model-based clustering framework grounded in elliptically symmetric distributions, introducing—for the first time—the angular Gaussian and projected spherical Cauchy distributions with elliptical symmetry. Parameter estimation is carried out via the expectation–maximization (EM) algorithm, and the framework naturally incorporates covariate analysis. Extensive simulations demonstrate that the method effectively identifies the optimal number of clusters with high computational efficiency. Its superior performance is further validated on real-world spherical and hyperspherical datasets, including earthquake locations, confirming its practical utility and robustness.

Abstract

Model--based clustering for directional data data has attracted a lot of interest, but most methods utilize rotationally symmetric distributions. This paper suggests the use of elliptically symmetric distributions, namely the elliptically symmetric angular Gaussian and the spherical elliptically symmetric projected Cauchy distributions that were recently proposed in the literature for modelling spherical data. The expectation--maximization algorithm is employed and the inclusion of covariates is also examined. Simulation studies compare the two distributions in terms of choosing the optimal number of clusters and computational cost. We use the mixtures of these two distributions to cluster two datasets on the sphere (earthquake locations) and two hyper--spherical datasets.

Problem

• model-based clustering
• directional data
• elliptically symmetric distributions
• spherical data
• hyper-spherical data

Innovation

• elliptically symmetric distributions
• model-based clustering
• directional data
• EM algorithm
• spherical data