Totally Balanced Dissimilarities

Abstract

We show in this paper a bijection between totally balanced hypergraphs 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.

An interval convexity-based framework for multilevel clustering with applications to single-linkage clustering

“…A hierarchy is a multilevel clustering for which the intersection of any two clusters is either empty or equal to one of them. In the last decades, several authors have investigated various generalizations of the hierarchical model, such as pyramids [17,19], paired hierarchies [7,8] and totally balanced hypergraphs [12,11]. These models are submodels of the weak hierarchical clustering model.…”