A Method for Comparing Two Hierarchical Clusterings

Abstract This article concerns the derivation and use of a measure of similarity between two hierarchical clusterings. The measure, Bk , is derived from the matching matrix, [mij ], formed by cutting the two hierarchical trees and counting the number of matching entries in the k clusters in each tree. The mean and variance of Bk are determined under the assumption that the margins of [mij ] are fixed. Thus, Bk represents a collection of measures for k = 2, …, n – 1. (k, Bk ) plots are found to be useful in portraying the similarity of two clusterings. Bk is compared to other measures of similarity proposed respectively by Baker (1974) and Rand (1971). The use of (k, Bk ) plots for studying clustering methods is explored by a series of Monte Carlo sampling experiments. An example of the use of (k, Bk ) on real data is given.