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\(n\)-way metrics. (English) Zbl 1337.54019

Summary: We study a family of \(n\)-way metrics that generalize the usual two-way metric. The \(n\)-way metrics are totally symmetric maps from \(E^n\) into \(\mathbb{R}_{\geq 0}\). The three-way metrics introduced by S. Joly and G. Le Calvé [J. Classif. 12, No. 2, 191–205 (1995; Zbl 0836.62046)] and W. J. Heiser and M. Bennani [J. Math. Psychol. 41, No. 2, 189–206 (1997; Zbl 1072.91639)] and the \(n\)-way metrics studied in [M. M. Deza and I. G. Rosenberg, Eur. J. Comb. 21, No. 6, 797–806 (2000; Zbl 0988.54029)] belong to this family. It is shown how the \(n\)-way metrics and \(n\)-way distance measures are related to \((n-1)\)-way metrics, respectively, \((n-1)\)-way distance measures.

MSC:

54E35 Metric spaces, metrizability
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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