Robust Improper Maximum Likelihood: Tuning, Computation, and a Comparison With Other Methods for Robust Gaussian Clustering

• 成果类型: Article
• 署名作者: Coretto, Pietro; Hennig, Christian
• 署名单位: University of Salerno; University of London; University College London
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1100996
• 发表日期: 2016
• 页码: 1648-1659
• 关键词: mixture; identification; estimators; point

摘要

The two main topics of this article are the introduction of the optimally tuned robust improper maximum likelihood estimator (OTRIMLE) for robust clustering based on the multivariate Gaussian model for clusters, and a comprehensive simulation study comparing the OTRIMLE to maximum likelihood in Gaussian mixtures with and without noise component, mixtures oft-distributions, and the TCLUST approach for trimmed clustering. The OTRIMLE uses an improper constant density for modeling outliers and noise. This can be chosen optimally so that the nonnoise part of the data looks as close to a Gaussian mixture as possible. Some deviation from Gaussianity can be traded in for lowering the estimated noise proportion. Covariance matrix constraints and computation of the OTRIMLE are also treated. In the simulation study, all methods are confronted with setups in which their model assumptions are not exactly fulfilled, and to evaluate the experiments in a standardized way by misclassification rates, a new model-based definition of true clusters is introduced that deviates from the usual identification of mixture components with clusters. In the study, every method turns out to be superior for one or more setups, but the OTRIMLE achieves the most satisfactory overall performance. The methods are also applied to two real datasets, one without and one with known true clusters. Supplementary materials for this article are available online.