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© 2014

Encyclopedia of Distances

Book

Table of contents

  1. Front Matter
    Pages i-xx
  2. Mathematics of Distances

    1. Front Matter
      Pages 1-1
    2. Michel Marie Deza, Elena Deza
      Pages 3-62
    3. Michel Marie Deza, Elena Deza
      Pages 63-70
    4. Michel Marie Deza, Elena Deza
      Pages 71-84
    5. Michel Marie Deza, Elena Deza
      Pages 85-94
    6. Michel Marie Deza, Elena Deza
      Pages 95-106
  3. Geometry and Distances

    1. Front Matter
      Pages 107-107
    2. Michel Marie Deza, Elena Deza
      Pages 109-131
    3. Michel Marie Deza, Elena Deza
      Pages 133-166
    4. Michel Marie Deza, Elena Deza
      Pages 167-180
    5. Michel Marie Deza, Elena Deza
      Pages 181-193
  4. Distances in Classical Mathematics

    1. Front Matter
      Pages 195-195
    2. Michel Marie Deza, Elena Deza
      Pages 197-212
    3. Michel Marie Deza, Elena Deza
      Pages 213-225
    4. Michel Marie Deza, Elena Deza
      Pages 227-244
    5. Michel Marie Deza, Elena Deza
      Pages 245-255
    6. Michel Marie Deza, Elena Deza
      Pages 257-272
  5. Distances in Applied Mathematics

    1. Front Matter
      Pages 273-273
    2. Michel Marie Deza, Elena Deza
      Pages 275-307

About this book

Introduction

This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances.

The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.

Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances.

As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who’s Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.

Keywords

distance metric space similarity

Authors and affiliations

  1. 1.Ecole Normale SupérieureParis CX 05France
  2. 2.Moscow State Pedagogical UniversityMoskvaRussia

Bibliographic information

Reviews

From the reviews of the second edition:

“This encyclopedia, dedicated to the theme ‘distances’ in the areas of pure mathematics up to abstract spaces, applied mathematics and applications, includes an impressive rich amount of different topics and knowledge areas. … The encyclopedia is highly recommended for students and researchers and everybody who is interested in increasing his knowledge on this fascinating field of distances.” (Gertraud Ehrig, Zentralblatt MATH, Vol. 1259, 2013)

“This is the second edition of the original text (2006). There are several additions, corrections and some streamlining has been done, but the general idea and structure is maintained. The concept of distance is interpreted in its broadest possible sense. In 29 chapters, the concept of distance is placed in as many different contexts by giving an enumeration of definition and properties. … The paper version is clearly a welcome asset in a mathematics library.” (A. Bultheel, The European Mathematical Society, December, 2012)