A local search approximation algorithm for k-means clustering

In k-means clustering we are given a set of n data points in d-dimensional space d and an integer k, and the problem is to determine a set of k points in d , called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomial-time algorithms are known for this problem. Although asymptotically efficient approximation algorithms exist, these algorithms are not practical due to the very high constant factors involved. There are many heuristics that are used in practice, but we know of no bounds on their performance. We consider the question of whether there exists a simple and practical approximation algorithm for k-means clustering. We present a local improvement heuristic based on swapping centers in and out. We prove that this yields a (9 + )-approximation algorithm. We present an example showing that any approach based on performing a fixed number of swaps achieves an approximation factor of at least (9 - ) in all sufficiently high di...

• Type: Journal
• Year: 2004
• Where: COMGEO
• Authors: Tapas Kanungo, David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman, Angela Y. Wu
• Keywords: Algorithm, Applied Computing, COMGEO 2004, Heuristic, K-means Clustering