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Encyclopedia of Distances

  • Michel Marie Deza
  • Elena Deza

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
    3. Michel Marie Deza, Elena Deza
      Pages 309-321
    4. Michel Marie Deza, Elena Deza
      Pages 323-339
    5. Michel Marie Deza, Elena Deza
      Pages 341-355
  6. Computer-Related Distances

    1. Front Matter
      Pages 357-357
    2. Michel Marie Deza, Elena Deza
      Pages 359-375
    3. Michel Marie Deza, Elena Deza
      Pages 377-385
    4. Michel Marie Deza, Elena Deza
      Pages 387-411
    5. Michel Marie Deza, Elena Deza
      Pages 413-428
  7. Distances in Natural Sciences

    1. Front Matter
      Pages 429-429
    2. Michel Marie Deza, Elena Deza
      Pages 431-485
    3. Michel Marie Deza, Elena Deza
      Pages 487-519
    4. Michel Marie Deza, Elena Deza
      Pages 521-560
    5. Michel Marie Deza, Elena Deza
      Pages 561-592
  8. Real-World Distances

    1. Front Matter
      Pages 593-593
    2. Michel Marie Deza, Elena Deza
      Pages 595-608
    3. Michel Marie Deza, Elena Deza
      Pages 609-659
    4. Michel Marie Deza, Elena Deza
      Pages 661-699
  9. Back Matter
    Pages 701-733

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

  • Michel Marie Deza
    • 1
  • Elena Deza
    • 2
  1. 1.Ecole Normale SupérieureParis CX 05France
  2. 2.Moscow State Pedagogical UniversityMoskvaRussia

Bibliographic information