Abstract Two matrix-variate distributions, both elliptical heavy-tailed generalization of the matrix-variate normal distribution, are introduced. They belong to the normal scale mixture family, and are respectively obtained by choosing a convenient shifted exponential or uniform as mixing distribution. Moreover, they have a closed-form for the probability density function that is characterized by only one additional parameter, with respect to the nested matrix-variate normal, governing the tail-weight. Both distributions are then used for model-based clustering via finite mixture models. The resulting mixtures, being able to handle data with atypical observations in a better way than the matrix-variate normal mixture, can avoid the disruption of the true underlying group structure. Different EM-based algorithms are implemented for parameter estimation and tested in terms of computational times and parameter recovery. Furthermore, these mixture models are fitted to simulated and real datasets, and their fitting and clustering performances are analyzed and compared to those obtained by other well-established competitors.

中文翻译：

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两个新的矩阵变量分布在基于模型的聚类中的应用

摘要 介绍了两个矩阵变量分布，它们都是矩阵变量正态分布的椭圆重尾推广。它们属于正常尺度混合族，分别通过选择一个方便的移位指数或均匀分布作为混合分布来获得。此外，它们具有概率密度函数的封闭形式，其特征在于只有一个附加参数，相对于嵌套矩阵变量正态，控制尾权重。然后通过有限混合模型将这两种分布用于基于模型的聚类。由此产生的混合物能够以比矩阵变量正常混合物更好的方式处理具有非典型观察的数据，可以避免破坏真正的基础组结构。不同的基于 EM 的算法用于参数估计，并在计算时间和参数恢复方面进行测试。此外，这些混合模型适用于模拟和真实数据集，并分析了它们的拟合和聚类性能，并将其与其他知名竞争对手获得的性能进行了比较。