Probabilistic k-median clustering in data streams

Abstract

We define the notion of coresets for probabilistic clustering problems and propose the first (k, ε)-coreset constructions for the probabilistic k-median problem in the metric and Euclidean case. The coresets are of size poly(ε-1, k, log(W/(wmin • pmin • δ))), where W is the expected total weight of the weighted probabilistic input points, wmin is the minimum weight of a probabilistic input point, pmin is the minimum realization probability, and δ is the error probability of the construction. We show how to maintain our coreset for Euclidean spaces in data streams. © Springer-Verlag 2013.