Robust linear clustering

• 成果类型: Article
• 署名作者: Garcia-Escudero, L. A.; Gordaliza, A.; San Martin, R.; Van Aelst, S.; Zamar, R.
• 署名单位: Universidad de Valladolid; Ghent University; University of British Columbia
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2008.00682.x
• 发表日期: 2009
• 页码: 301-318
• 关键词: self-consistency; fast algorithm; identification; methodology; features; datasets; xgobi

摘要

Non-hierarchical clustering methods are frequently based on the idea of forming groups around 'objects'. The main exponent of this class of methods is the k-means method, where these objects are points. However, clusters in a data set may often be due to certain relationships between the measured variables. For instance, we can find linear structures such as straight lines and planes, around which the observations are grouped in a natural way. These structures are not well represented by points. We present a method that searches for linear groups in the presence of outliers. The method is based on the idea of impartial trimming. We search for the 'best' subsample containing a proportion 1-alpha of the data and the best k affine subspaces fitting to those non-discarded observations by measuring discrepancies through orthogonal distances. The population version of the sample problem is also considered. We prove the existence of solutions for the sample and population problems together with their consistency. A feasible algorithm for solving the sample problem is described as well. Finally, some examples showing how the method proposed works in practice are provided.