Totally Balanced Dissimilarities

François Brucker (1) , Pascal Prea (1) , Célia Châtel (2)

1 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
2 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)

We show in this paper a bijection between totally balanced hy-pergraphs and so called totally balanced dissimilarities. We give an efficient way (O(n 3) where n is the number of elements) to (i) recognize if a given dissimilarity is totally balanced and (ii) approximate it if it is not the case. We also introduce a new kind of dissimilarity which generalize chordal graphs and allows a polynomial number of cluster that can be easily computed and interpreted.

Domaines: Mathématique discrète [cs.DM]; Géométrie algorithmique [cs.CG]; Algorithme et structure de données [cs.DS]; Combinatoire [math.CO]; Géométrie métrique [math.MG]

François Brucker, Pascal Prea, Célia Châtel. Totally Balanced Dissimilarities. Journal of Classification, 2019, ⟨10.1007/s00357-019-09320-w⟩. ⟨hal-02269391⟩