Model--based clustering for spherical and hyper--spherical data using elliptically symmetric distributions
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.
Related
- Symmetric power L-functions of a weighted hyper-Kloosterman family
- Robust model-based clustering via mixtures of multivariate pseudo-Voigt distributions
- Spherical maximal operators on rank one Riemannian symmetric spaces of noncompact type
- Approximating the Gibbs Measure of Spherical Spin Glasses to Within o(N−1/2) in the Replica Symmetric Phase
- Joint distributions of eigenvectors of symmetric random tensors
BibTeX
@misc{perdikis2026modelbased,
title = {{Model--based clustering for spherical and hyper--spherical data using elliptically symmetric distributions}},
author = {Theodoros Perdikis and Nader Alharbi and Michail Tsagris},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.27496},
eprint = {2605.27496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.27496},
note = {CC0},
}
RIS
TY - UNPB
TI - Model--based clustering for spherical and hyper--spherical data using elliptically symmetric distributions
AU - Theodoros Perdikis
AU - Nader Alharbi
AU - Michail Tsagris
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2605.27496
UR - https://arxiv.org/abs/2605.27496
AB - 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.
ER -