A general trimming approach to robust cluster analysis

• 成果类型: Article
• 署名作者: Garcia-Escudero, Luis A.; Gordaliza, Alfonso; Matran, Carlos; Mayo-Iscar, Agustin
• 署名单位: Universidad de Valladolid
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS515
• 发表日期: 2008
• 页码: 1324-1345
• 关键词: maximum-likelihood; k-means; orthogonal regression; em algorithm; scales

摘要

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion alpha of contaminating data to guarantee the robustness of the method. As a characteristic feature, restrictions on the ratio between the maximum and the minimum eigenvalues of the groups scatter matrices are introduced. This makes the problem to be well defined and guarantees the consistency of the sample solutions to the population ones. The method covers a wide range of clustering approaches depending on the strength of the chosen restrictions. Our proposal includes an algorithm for approximately solving the sample problem.