Comparison of hierarchical classifications

Abstract

Critchley and Van Cutsem [7J recently developed the properties of dissimi- larities and ultrametries with values in an ordered set. This theoretical· definition allows consideration of a pair of ultrametrics as a two dimensional ultrametrie with values in lR+ x lR+, and provides a good framework to study the dependence between two ultramet- ries. In this paper, we just present the basie definitions for introducing the definition of some new indices of dependence or of comparison of two real-valued ultrametrics. Details can be found in Benkaraache's thesis [4J.