n-Way Metrics

Matthijs J. Warrens

doi:10.1007/s00357-010-9052-x

n-Way Metrics

Matthijs J. Warrens^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

10 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	173-190
Number of pages	18
Journal	Journal of Classification
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s00357-010-9052-x
Publication status	Published - 2010
Externally published	Yes

Keywords

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

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PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - n-Way distance measure

KW - Parametrized inequality

KW - Tetrahedron inequality;Polyhedron inequality

KW - Triangle inequality

UR - http://www.scopus.com/inward/record.url?scp=77957021313&partnerID=8YFLogxK

U2 - 10.1007/s00357-010-9052-x

DO - 10.1007/s00357-010-9052-x

M3 - Article

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VL - 27

SP - 173

EP - 190

JO - Journal of Classification

JF - Journal of Classification

SN - 0176-4268

IS - 2

ER -

n-Way Metrics

Abstract

Keywords

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