This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that integrate 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 approximate 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.

中文翻译：

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实椭圆偏态分布及其在鲁棒聚类分析中的应用


本文提出了一类新的实椭圆偏斜 (RESK) 分布和相关的聚类算法，将鲁棒性和偏斜性集成到单个统一的聚类分析框架中。非对称分布和重尾数据集群已在各种实际应用中得到报道。稳健性至关重要，因为一些外围观察结果可能会严重掩盖簇结构。 RESK 分布是实椭圆对称 (RES) 分布的推广。为了估计簇参数和成员资格，我们推导了任意 RESK 分布的期望最大化 (EM) 算法。特别关注一个新的鲁棒 skew-Huber M 估计器，它也是 skew-Huber 分布的近似最大似然估计器 (MLE)，属于 RESK 类。对模拟和真实数据的数值实验证实了所提出的方法对于倾斜和重尾数据集的有用性。