Title: The Effectiveness of Lloyd-type Methods for the k-Means Problem

                 Chaitanya Swamy
   Center for the Mathematics of Information
       California Institute of Technology

ABSTRACT:  We consider the k-means problem: given a set of n data points in
a high dimensional Euclidean space, find k "centers" (points in the space)
so as to minimize the sum of the squared distances from each data point to
its nearest center. We investigate a widely-used iterative heuristic for
this problem, called Lloyd's method (or Lloyd-type method), in an attempt to
explain its popularity among practitioners, and in order to suggest
improvements in its application. We propose and justify a clusterability
criterion for data sets, and show that a simple Lloyd-type method quickly
leads to provably near-optimal solutions on well-clusterable instances. This
is the first performance guarantee for any variant of Lloyd's heuristic.
Furthermore, some of our algorithms are candidates for being faster in
practice than currently used variants of Lloyd's method. The main
algorithmic contribution is a novel probabilistic seeding process for the
starting configuration of a Lloyd-type iteration, which leads to the desired
performance guarantee. The talk will be self contained.

This is joint work with Rafail Ostrovsky, Yuval Rabani and Leonard Schulman.