Journal of Classification

, Volume 27, Issue 2, pp 173–190 | Cite as

n-Way Metrics

  • Matthijs J. Warrens


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 \( {\mathbb{R}_{ \geqslant 0}} \). The three-way metrics introduced by Joly and Le Calvé (1995) and Heiser and Bennani (1997) and the n-way metrics studied in Deza and Rosenberg (2000) 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.


n-Way distance measure Triangle inequality Tetrahedron inequality;Polyhedron inequality Parametrized inequality 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Psychology, Unit Methodology and StatisticsLeiden UniversityLeidenThe Netherlands

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