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The geometry of triadic distances. (English) Zbl 1112.62328

Summary: Triadic distances \(t\) defined as functions of the Euclidean (dyadic) distances \(a_1, a_2, a_3\) between three points are studied. Special attention is paid to the contours of all points giving the same value of \(t\) when \(a-3\) is kept constant. These isocontours allow some general comments to be made about the suitability, or not, for practical investigations of certain definitions of triadic distance. We are especially interested in those definitions of triadic distance, designated as canonical, that have optimal properties. An appendix gives some results we have found useful.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
91C99 Social and behavioral sciences: general topics
62H99 Multivariate analysis
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