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Real Elliptically Skewed Distributions and Their Application to Robust Cluster Analysis

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Document pages: 22 pages

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

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