基于简约污染混合模型的高维无监督分类
High-dimensional unsupervised classification via parsimonious contaminated mixtures
摘要：
污染高斯分布代表高斯分布的一个简单的重尾椭圆推广;与经常考虑的t分布不同，它还允许自动检测轻微的离群点或“坏”点，其方式与观察通常分配给有限混合模型上下文中的组相同。从这个分布出发，我们提出了污染因子分析模型作为降维和检测更高维度的坏点的方法。混合污染高斯因子分析器（MCGFA）模型如下，并扩展最近提出的混合污染高斯分布的高维数据。我们介绍了一个家庭的32个简约的模型，通过引入一般MCGFA模型的协方差和污染结构的约束。我们概述了参数估计的期望最大化算法的一个变体。各种实施问题进行了讨论，和新的家庭的模型相比，成熟的方法模拟和真实的数据。
英文摘要：
The contaminated Gaussian distribution represents a simple heavy-tailed elliptical generalization of the Gaussian distribution; unlike the often-considered t-distribution, it also allows for automatic detection of mild outlying or "bad" points in the same way that observations are typically assigned to the groups in the finite mixture model context. Starting from this distribution, we propose the contaminated factor analysis model as a method for dimensionality reduction and detection of bad points in higher dimensions. A mixture of contaminated Gaussian factor analyzers (MCGFA) model follows therefrom, and extends the recently proposed mixture of contaminated Gaussian distributions to high-dimensional data. We introduce a family of 32 parsimonious models formed by introducing constraints on the covariance and contamination structures of the general MCGFA model. We outline a variant of the expectation-maximization algorithm for parameter estimation. Various implementation issues are discussed, and the novel family of models is compared to well-established approaches on both simulated and real data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
