Fast Algorithms for Constant Approximation k-Means Clustering

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 )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(k3 n2 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(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.

• Type: Journal
• Year: 2010
• Where: MLDM
• Authors: Mingjun Song, Sanguthevar Rajasekaran
• Keywords: Algorithm, Approximation Algorithms, K-means, Machine Learning, MLDM 2010