Mixtures of Matrix-Variate Contaminated Normal Distributions

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 <i>a posteriori</i> 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.

矩阵变量数据（matrix-variate data）的分析在学术文献中愈发常见，尤其集中于聚类与分类领域。真实数据（含真实矩阵变量数据）往往会受到潜在异常观测值的污染。鉴于这类数据在有效可视化方面存在实际应用挑战，对异常值的检测以及开发对异常值鲁棒的模型，对这类数据而言尤为关键。本文首先探讨了矩阵变量污染正态分布（matrix-variate contaminated normal distribution），随后将其应用于聚类的混合模型范式中。所提模型的核心优势之一，是可通过计算各矩阵属于典型或非典型的后验概率（a posteriori probability），自动识别潜在异常矩阵。现有矩阵变量方法目前尚不具备此类检测能力。本文采用条件期望最大化算法（expectation conditional maximization algorithm）进行参数估计，并通过模拟数据与真实数据展开示例验证。本文的补充材料可在线获取。