Algorithmica

pp 1–20

Improved Analysis of Complete-Linkage Clustering

Article

DOI: 10.1007/s00453-017-0284-6

Cite this article as:
Großwendt, A. & Röglin, H. Algorithmica (2017). doi:10.1007/s00453-017-0284-6
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Abstract

Complete-linkage clustering is a very popular method for computing hierarchical clusterings in practice, which is not fully understood theoretically. Given a finite set \(P\subseteq \mathbb {R}^d\) of points, the complete-linkage method starts with each point from P in a cluster of its own and then iteratively merges two clusters from the current clustering that have the smallest diameter when merged into a single cluster. We study the problem of partitioning P into k clusters such that the largest diameter of the clusters is minimized and we prove that the complete-linkage method computes an O(1)-approximation for this problem for any metric that is induced by a norm, assuming that the dimension d is a constant. This improves the best previously known bound of \(O(\log {k})\) due to Ackermann et al. (Algorithmica 69(1):184–215, 2014). Our improved bound also carries over to the k-center and the discrete k-center problem.

Keywords

Clustering Complete-linkage Hierarchical clustering Approximation algorithms Diameter k-clustering problem Discrete k-center problem 

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BonnBonnGermany