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Patrice Bertrand

Patrice Bertrand

Université Paris-Dauphine, PSL Research University, PARIS, FRANCE

Title: Multilevel clustering models and dissimilarities

Biography

Biography: Patrice Bertrand

Abstract

Overlapping clustering is a clustering structure in which objects may belong to more than one cluster. New multilevel clustering models, which were mostly introduced during the 1980’s, include overlapping clusters and extend he well-known Benzécri-Johnson bijection. This talk is concerned with the characterization of such various multilevel clustering models within the framework of general convexity. Along this line, both the paired hierarchical model and the k-weakly hierarchical models for k ≥ 3, are characterized as interval convexities. Sufficient conditions are provided for an interval convexity to be either hierarchical, paired hierarchical, pyramidal, weakly hierarchical or k-weakly hierarchical. In addition, an algorithm is introduced for computing the interval convexity induced by any given interval operator. A general clustering algorithm is then derived to build any of the previously considered multilevel clustering models. This approach is illustrated by considering specific parameterized interval operators, that can be defined from any dissimilarity index, and selected in an adaptive way.