Abstract
In this paper, dissimilarity relations are defined on triples rather than on dyads. We give a definition of a three-way distance analogous to that of the ordinary two-way distance. It is shown, as a straightforward generalization, that it is possible to define three-way ultrametric, three-way star, and three-way Euclidean distances. Special attention is paid to a model called the semi-perimeter model.
We construct new methods analogous to the existing ones for ordinary distances, for example: principal coordinates analysis, the generalized Prim (1957) algorithm, hierarchical cluster analysis.
Resume
Cet article traite de relations de dissimilarité définies sur des triplets au lieu de couples. Nous donnons une définition de la distance à trois voies analogue à celle de la distance habituelle entre deux points. On montre qu’une généralisation naturelle permet de définir les notions d’ultramétrique à trois voies, distance à centre à trois voies, et distances Euclidiennes à trois voies. Une attention particulière est portée au modèle dénommé demi périmètre.
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Joly, S., Le Calvé, G. Three-way distances. Journal of Classification 12, 191–205 (1995). https://doi.org/10.1007/BF03040855
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DOI: https://doi.org/10.1007/BF03040855