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Zbl 0846.62047
Bertrand, P.
Properties and topological characterizations of a pyramidal representation. (Propriétés et caractérisations topologiques d'une représentation pyramidale.) (French)
[J] Math. Inf. Sci. Hum. 117, 5-28 (1992). ISSN 0995-2314

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 2000:: *62H30 Statistical classification, etc.
91C20 Clustering

Keywords: geometric characteristics; Robinsonian dissimilarities; proximity measures; total order; segment; boundary

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