On the stability of hierarchical classification: Qualitative approaches

Authors:
Jean-Pierre BarthéLemy;Gentian Gusho
Affiliations:
Département Logique des Usages, Sciences Sociales et de l'Information, Ecole Nationale Supérieure des Télécommunications de Bretagne, Technopôle de Brest-Iroise, CS 83818, ...;Département Logique des Usages, Sciences Sociales et de l'Information, Ecole Nationale Supérieure des Télécommunications de Bretagne, Technopôle de Brest-Iroise, CS 83818, ...
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 3
Cited 0

Models of incremental concept formation

Machine learning: paradigms and methods
Axiomatic Concensus Theory in Group Choice and Biomathematics (Frontiers in Applied Mathematics, 29)

Axiomatic Concensus Theory in Group Choice and Biomathematics (Frontiers in Applied Mathematics, 29)
Stability conditions for consensus functions defined on n-trees

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.98

Visualization

Abstract

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).