Abstract (EN)

The weakly indexed paired-hierarchies (shortly, p-hierarchies) providea clustering model that allows overlapping clusters and extends the hierarchicalmodel. There exists a bijection between weakly indexed p-hierarchies and the so-called paired-ultrametrics (shortly, p-ultrametrics), this correspondence being a re-striction of the bijection between weakly indexed pyramids and Robinsonian dis-similarities. This paper proposes a generalization of the well-known HAC clusteringmethod to compute a weakly indexed p-hierarchy from a given dissimilarity d. More-over, the p-ultrametric associated to such a weakly indexed p-hierarchy is provedto be lower-maximal for d and larger than the sub-dominant ultrametric of d.