EFFICIENT ALGORITHMS FOR DIVISIVE HIERARCHICAL-CLUSTERING WITH THE DIAMETER CRITERION

Divisive hierarchical clustering algorithms with the diameter criterion 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 O(MBAR N2) and O(N2 log N) respectively, where MBAR 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 MBAR clusters and is in O(N2) for fixed MBAR. 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 1/2 less-than-or-equal-to p < 1, it provides a complete hierarchy of partitions in O(N2 log N) time. The latter algorithm, a refinement of an algorithm of Rao, allows to build a complete hierarchy of partitions in O(N2 log N) time without any restriction. Comparative computational experiments with both algorithms and with an agglomerative hierarchical algorithm of Benzecri are reported.