An overall index for comparing hierarchical clusterings

In this paper we suggest a new index for measuring thedistance between two hierarchical clusterings. This index can bedecomposed into the contributions pertaining to each stage of thehierarchies. We show the relations of such components with thecurrently used criteria for comparing two partitions. We obtain asimilarity index as the complement to one of the suggesteddistance and we propose its adjustment for agreement due tochance. We consider the extension of the proposed distance andsimilarity measures to more than two dendrograms and their use forthe consensus of classification and variable selection in clusteranalysis.