An Overall Index for Comparing Hierarchical Clusterings

Abstract In this paper we suggest a new index for measuring the distance between two hierarchical clusterings. This index can be decomposed into the contributions pertaining to each stage of the hierarchies. We show the relations of such com-ponents with the currently used criteria for comparing two partitions. We obtain a similarity index as the complement to one of the suggested distances and we propose its adjustment for agreement due to chance. We consider the extension of the proposed distance and similarity measures to more than two dendrograms and their use for the consensus of classification and variable selection in cluster analysis.