Fast k-means algorithms with constant approximation

Abstract

In this paper we study the k-means clustering problem. It is well-known that the general version of this problem is NP-hard. Numerous approximation algorithms have been proposed for this problem. In this paper, we proposed three constant approximation algorithms for k-means clustering. The first algorithm runs in time O((k/ε)knd), where k is the number of clusters, n is the size of input points, d is dimension of attributes. The second algorithm runs in time O(k3n2 log n). This is the first algorithm for k-means clustering that runs in time polynomial in n, k and d. The run time of the third algorithm (O(k5 log3 kd)) is independent of n. Though an algorithm whose run time is independent of n is known for the k-median problem, ours is the first such algorithm for the k-means problem. © Springer-Verlag Berlin Heidelberg 2005.