Strong consistency of k-parameters clustering

JOURNAL OF MULTIVARIATE ANALYSIS

卷:117

Article

Gallegos, Maria Teresa¹  Ritter, Gunter^1,2 

[1] Inst Data Anal, D-94121 Salzweg, Germany

[2] Univ Passau, Fac Informat & Math, D-94030 Passau, Germany

关键词: Cluster analysis;    Classification models;    Elliptical models;    Maximum likelihood estimation;    Strong consistency;   

DOI  :  10.1016/j.jmva.2013.01.013

来源: Elsevier

【 摘 要 】

Pollard showed for k-means clustering and a very broad class of sampling distributions that the optimal cluster means converge to the solution of the related population criterion as the size of the data set increases. We extend this consistency result to k-parameters clustering, a method derived from the heteroscedastic, elliptical classification model. It allows a more sensitive data analysis and has the advantage of being affine equivariant. Moreover, the present theory yields a consistent criterion for selecting the number of clusters in such models. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free