An order theoretic framework for overlapping clustering
Discrete Mathematics - Special issue: trends in discrete mathematics
Triadic distance models: axiomatization and least squares representation
Journal of Mathematical Psychology
Quasi-ultrametrics and their 2-ball hypergraphs
Proceedings of the conference on Discrete metric spaces
The k-weak hierarchical representations: an extension of the indexed closed weak hierarchies
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Hi-index | 0.04 |
Multiway dissimilarities are a natural generalization of standard pairwise ones, that allow global comparison of more than two entities. Assuming the entity descriptions belong to a complete meet-semilattice, we consider so-called description-meet compatible multiway dissimilarities on the entity set; that is, multiway dissimilarities agreeing with entity descriptions in the following sense: the lower the greatest lower bound of the descriptions of entities in a given subset, the more dissimilar the entities in this subset. On the one hand, we show that when the entity description set is of breadth k, strictly description-meet compatible k-way dissimilarities are quasi-ultrametric. By duality, when entity descriptions belong to a complete join-semilattice, a similar result holds for so-called strictly description-join compatible multiway dissimilarities. Moreover, we study relationships between multiway dissimilarities in general, and provide examples of description-meet compatible ones.