n-Way Metrics

Matthijs J. Warrens*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)


We study a family of n-way metrics that generalize the usual two-way metric. The n-way metrics are totally symmetric maps from En into ℝ≥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.

Original languageEnglish
Pages (from-to)173-190
Number of pages18
JournalJournal of Classification
Issue number2
Publication statusPublished - 2010
Externally publishedYes


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

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