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Metric Transforms of L1-Spaces

  • Michel Marie Deza
  • Monique Laurent
Part of the Algorithms and Combinatorics book series (AC, volume 15)

Abstract

Let (X,d) be a distance space and let F: ℝ+ → ℝ+ be a function such that F(0) = 0. We define the distance space (X,F(d)) by setting
$$F{\left( d \right)_{ij}} = F\left( {{d_{ij}}} \right)\;for\;all\;i,j \in X.$$
(9.0.1)
Following Blumenthal [1953], (X,F(d)) is called a metric transform of (X,d). A general question is to find nontrivial functions F which preserve certain properties, such as metricity, L 1- or L 2-embeddability, of the original distance space.

Keywords

Positive Semidefinite Power Transform Distance Space Cardinality Measure Negative Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Michel Marie Deza
    • 1
    • 2
  • Monique Laurent
    • 1
    • 3
  1. 1.Département de Mathématiques et d’InformatiqueLaboratoire d’Informatique de l’Ecole Normale SupérieureParis Cedex 05France
  2. 2.Department of MathematicsMoscow Pedagogical State UniversityMoscowRussia
  3. 3.CWIAmsterdamThe Netherlands

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