Real Elliptically Skewed Distributions and Their Application to Robust Cluster Analysis

TL;DR

This paper introduces a new class of distributions called RESK, along with clustering algorithms that incorporate robustness and skewness, improving analysis of skewed, heavy-tailed data in real-world applications.

Contribution

It proposes the RESK distribution class and develops an EM algorithm for robust clustering, including a new skew-Huber M-estimator for skewed, heavy-tailed data.

Findings

RESK distributions effectively model skewed, heavy-tailed data.

The EM algorithm accurately estimates cluster parameters.

Numerical experiments demonstrate improved clustering performance.

Abstract

This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that allow for integrating robustness and skewness into a single unified cluster analysis framework. Non-symmetrically distributed and heavy-tailed data clusters have been reported in a variety of real-world applications. Robustness is essential because a few outlying observations can severely obscure the cluster structure. The RESK distributions are a generalization of the Real Elliptically Symmetric (RES) distributions. To estimate the cluster parameters and memberships, we derive an expectation maximization (EM) algorithm for arbitrary RESK distributions. Special attention is given to a new robust skew-Huber M-estimator, which is also the maximum likelihood estimator (MLE) for the skew-Huber distribution that belongs to the RESK class. Numerical experiments on simulated and real-world data confirm the usefulness of the proposed methods for skewed and heavy-tailed data sets.