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# Efficient Algorithms for Divisive Hierarchical Clustering with the Diameter Criterion

## A Guenoche, Pierre Hansen, and Brigitte Jaumard

BibTeX reference

Divisive hierarchical clustering algorithms with the diametercriterion proceed by recursively selecting the cluster with largest diameter and partitioning it into two clusters whose largest diameter is smallest possible. We provide two such algorithms with complexities and respectively, where denotes the maximum number of clusters in a partition and N the number of entities to be clustered. The former algorithm, an efficient implementation of an algorithm of Hubert, allows to find all partitions into at most clusters and is in for fixed . Moreover, if in each partitioning the size of the largest cluster is bounded by p times the number of entities in the set to be partitioned, with , it provides a complete hierarchy of partitions in time. The latter algorithm, a refinement of an algorithm of Rao, allows to build a complete hierarchy of partitions in time without any restriction. Comparative computational experiments with both algorithms and with an agglomerative hierarchical algorithm of Benzécri are reported.

, 31 pages

This cahier was revised in August 1990