Abstract (EN)

Clustering systems with or without overlapping clusters and their dissimilarities. The bijection of Benzécri and Johnson sets up a one-one correspondence between hierarchical clusterings and ultrametric dissimilarities [Johnson, 1967 ; Benzécri, 1973]. New clustering structures, which were introduced during the 1980's, include overlapping clusters and extend this bijection. In this text, we are concerned with a general framework that enables us to represent and compare several previously proposed extensions of the bijection of Benzécri and Johnson. We consider, more particularly, the extensions of this bijection that exist between certain general types of clustering systems that include overlapping clusters, on one hand, and the set of all the dissimilarities, on the other hand.