Strong consistency of k-parameters clustering

Authors:
MaríA Teresa Gallegos;Gunter Ritter
Affiliations:
Institute for Data Analysis, D-94121 Salzweg, Germany;Institute for Data Analysis, D-94121 Salzweg, Germany and Faculty of Informatics and Mathematics, University of Passau, D-94030 Passau, Germany
Venue:
Journal of Multivariate Analysis
Year:
2013

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Abstract

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.