ABSTRACT

Analysis of matrix-variate data is becoming ever more prevalent in the literature, especially in the area of clustering and classification. Real data, including real matrix-variate data, are often contaminated by potential outlying observations. Their detection, as well as the development of models insensitive to their presence, is particularly important for this type of data because of the practical issues concerning their effective visualization. Herein, the matrix-variate contaminated normal distribution is discussed and then utilized in the mixture model paradigm for clustering. One key advantage of the proposed model is the ability to automatically detect potential outlying matrices by computing their a posteriori probability of being typical or atypical. Such detection is currently unavailable using existing matrix-variate methods. An expectation conditional maximization algorithm is used for parameter estimation, and both simulated and real data are used for illustration. Supplementary files for this article are available online.

摘要

矩阵变量数据的分析在文献中变得越来越普遍，特别是在聚类和分类领域。真实数据，包括真实矩阵变量数据，经常被潜在的异常观察所污染。由于与有效可视化有关的实际问题，它们的检测以及对其存在不敏感的模型的开发对于此类数据尤为重要。在此，讨论了矩阵变量污染正态分布，然后将其用于混合模型范例进行聚类。所提出模型的一个关键优势是能够通过计算后验来自动检测潜在的离群矩阵是典型或非典型的概率。这种检测目前无法使用现有的矩阵变量方法进行。使用期望条件最大化算法进行参数估计，并使用模拟数据和真实数据进行说明。本文的补充文件可在线获取。