PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Stability of k-means clustering
Shai Ben-David, David Pal and Hans Simon
Proceedings of COLT 2007 2007.


We consider the stability of $k$-means clustering problems. Clustering stability is a common heuristics used to determine the number of clusters in a wide variety of clustering applications. We continue the theoretical analysis of clustering stability by establishing a complete characterization of clustering stability in terms of the number of optimal solutions to the clustering optimization problem. Our results complement earlier work of Ben-David, von Luxburg and P\'al, by settling the main problem left open there. Our analysis shows that, for probability distributions with finite support, the stability of $k$-means clusterings depends solely on the number of optimal solutions to the underlying optimization problem for the data distribution. These results challenge the common belief and practice that view stability as an indicator of the validity, or meaningfulness, of the choice of a clustering algorithm and number of clusters.

PDF - Requires Adobe Acrobat Reader or other PDF viewer.
EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2385
Deposited By:Hans Simon
Deposited On:22 November 2006