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Description-meet compatible multiway dissimilarities. (English) Zbl 1159.62355

Summary: 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.

MSC:

62P99 Applications of statistics
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