Smaller Coresets for k-Median and k-Means Clustering

Authors:
Sariel Har-Peled;Akash Kushal
Affiliations:
Department of Computer Science, University of Illinois, 201 N. Goodwin Avenue, Urbana, IL 61801, USA;Department of Computer Science, University of Illinois, 201 N. Goodwin Avenue, Urbana, IL 61801, USA
Venue:
Discrete & Computational Geometry
Year:
2007

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Abstract

In this paper we show that there exists a $(k,\varepsilon)$-coreset for k-median and k-means clustering of n points in ${\cal R}^d,$ which is of size independent of n. In particular, we construct a $(k,\varepsilon)$-coreset of size $O(k^2/\varepsilon^d)$ for k-median clustering, and of size $O(k^3/\varepsilon^{d+1})$ for k-means clustering.