Fast Algorithms for Constant Approximation k-Means Clustering
Mingjun Song, Sanguthevar Rajasekaran · 2010
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 propose three constant approximation algorithms for k-means clustering. The first algorithm runs in time O(( k )nd), where k is the number of clusters, n is the size of input points, and d is dimension of attributes. The second algorithm runs in time O(kn log n). This is the first algorithm for k-means clustering that runs in time polynomial in n, k and d simultaneously. The run time of the third algorithm ( O(k log 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.