On Lower-Maximal Paired-Ultrametrics.

The weakly indexed paired-hierarchies (shortly, p-hierarchies) provide a clustering model that allows overlapping clusters and extends the hierarchical model. There exists a bijection between weakly indexed p-hierarchies and the so-called paired-ultrametrics (shortly, p-ultrametrics), this correspondence being a restriction of the bijection between weakly indexed pyramids and Robinsonian dissimilarities. This paper proposes a generalization of the well-known HAC clustering method to compute a weakly indexed p-hierarchy from a given dissimilarity d. Moreover, the p-ultrametric associated to such a weakly indexed p-hierarchy is proved to be lower-maximal for d and larger than the sub-dominant ultrametric of d. [ABSTRACT FROM AUTHOR]