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Properties and topological characterizations of a pyramidal representation. (Propriétés et caractérisations topologiques d’une représentation pyramidale.) (French) Zbl 0846.62047

Summary: This paper presents some geometric characteristics of Robinsonian dissimilarities. These dissimilarities make up a very general model for representing proximity measures between objects (or groups of objects) when these entities are ranked according to a total order. Geometric properties of Robinsonian dissimilarities are presented with the help of the concepts of segment and boundary which are introduced for an arbitrary dissimilarity. We then focus on the set of Robinsonian dissimilarities without any ultrametric triplet; this set is dense in the set of Robinsonian dissimilarities, and can easily be characterized by geometric conditions.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
91C20 Clustering in the social and behavioral sciences
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