On the stability of hierarchical classification: Qualitative approaches

The aim of this paper is to study various forms of stability of clustering methods in a hierarchical and qualitative framework. It is based on two notions of the restriction of a hierarchy to a subset of objects. The first section discusses some properties of these notions of restriction. The second section gives ten axioms to describe the notion of stability. The last section establishes an impossibility theorem: there is no stable clustering method (except for very small cases).