The Effectiveness of Lloyd-Type Methods for the k-Means Problem
Rafail Ostrovsky; Yuval Rabani; Leonard J. Schulman; Chaitanya Swamy
Foundations of Computer Science, 2006. FOCS apos;06. 47th Annual IEEE Symposium on
Volume , Issue , Oct. 2006 Page(s):165 - 176
Digital Object Identifier 10.1109/FOCS.2006.75
Summary:We investigate variants of Lloyd's heuristic for clustering high dimensional data in an attempt to explain its popularity (a half century after its introduction) among practitioners, and in order to suggest improvements in its application. We propose and justify a clusterability criterion for data sets. We present variants of Lloyd's heuristic that quickly lead to provably near-optimal clustering solutions when applied to well-clusterable instances. This is the first performance guarantee for a variant of Lloyd's heuristic. The provision of a guarantee on output quality does not come at the expense of speed: some of our algorithms are candidates for being faster in practice than currently used variants of Lloyd's method. In addition, our other algorithms are faster on well-clusterable instances than recently proposed approximation algorithms, while maintaining similar guarantees on clustering quality. Our main algorithmic contribution is a novel probabilistic seeding process for the starting configuration of a Lloyd-type iteration
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