Analysis of Agglomerative Clustering

The diameter k-clustering problem is the problem of partitioning a finite subset of Rd into k subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem for all values of k is the agglomerative clustering algorithm with the complete linkage strategy. For decades this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension d is a constant, we show that for any k the solution computed by this algorithm is an O(log k)-approximation to the diameter k-clustering problem. Moreover, our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm. 1998 ACM Subject Classification F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Geometrical prob...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Marcel R. Ackermann, Johannes Blömer, Daniel Kuntze, Christian Sohler
• Keywords: Agglomerative Clustering, Algorithms, Complete Linkage, CORR 2010, Education