The Geometry of triadic distances

de Rooij, Mark and Gower, John C. (2003). The Geometry of triadic distances. Journal of Classification, 20(2) pp. 181–220.

DOI: https://doi.org/10.1007/s00357-003-0012-6

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Abstract

Triadic distances t defined as functions of the Euclidean (dyadic) distances a1, a2, a3 between three points are studied. Special attention is paid to the contours of all points giving the same value of t when a3 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.

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