Computing hierarchies of clusters from the euclidean minimum spanning tree in linear time

Abstract

A new hierarchical clustering method for point sets is presented, called diameter clustering, whose clusters belong to most other natural clusterings. For each cluster it holds that its diameter is small compared to the distance to a nearest point outside the cluster. Given a Euclidean minimum spanning tree of the input point set, it is shown that the diameter clustering can be computed in linear time. In addition we derive a nice property of this hierarchy which makes it particularly useful as a building block. It is shown in this paper that it can be employed to obtain a good approximation for the known single linkage clustering in roughly linear time. Other examples of its usefulness include computing the greedy triangulation, the complete linkage hierarchy, and a data structure for faster range queries.