Model-based clustering and classification using mixtures of multivariate skewed power exponential distributions

TL;DR

This paper introduces a new family of mixture models combining skewness and flexible tail behavior, improving clustering and classification of complex data compared to traditional Gaussian mixtures.

Contribution

It proposes skewed power exponential mixture models that enhance robustness and flexibility in modeling skewed and heavy-tailed data, with novel estimation algorithms.

Findings

Outperforms Gaussian mixtures in clustering tasks.

Effectively models skewness and tail variations.

Demonstrates advantages on simulated and benchmark datasets.

Abstract

Families of mixtures of multivariate power exponential (MPE) distributions have been previously introduced and shown to be competitive for cluster analysis in comparison to other elliptical mixtures including mixtures of Gaussian distributions. Herein, we propose a family of mixtures of multivariate skewed power exponential distributions to combine the flexibility of the MPE distribution with the ability to model skewness. These mixtures are more robust to variations from normality and can account for skewness, varying tail weight, and peakedness of data. A generalized expectation-maximization approach combining minorization-maximization and optimization based on accelerated line search algorithms on the Stiefel manifold is used for parameter estimation. These mixtures are implemented both in the model-based clustering and classification frameworks. Both simulated and benchmark data are used for illustration and comparison to other mixture families.