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Encyclopedia of Distances

  • Michel Marie Deza
  • Elena Deza

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Mathematics of Distances

    1. Front Matter
      Pages 1-1
    2. Michel Marie Deza, Elena Deza
      Pages 3-58
    3. Michel Marie Deza, Elena Deza
      Pages 59-66
    4. Michel Marie Deza, Elena Deza
      Pages 67-78
    5. Michel Marie Deza, Elena Deza
      Pages 79-87
    6. Michel Marie Deza, Elena Deza
      Pages 89-99
  3. Geometry and Distances

    1. Front Matter
      Pages 101-101
    2. Michel Marie Deza, Elena Deza
      Pages 103-123
    3. Michel Marie Deza, Elena Deza
      Pages 125-155
    4. Michel Marie Deza, Elena Deza
      Pages 157-168
    5. Michel Marie Deza, Elena Deza
      Pages 169-180
  4. Distances in Classical Mathematics

    1. Front Matter
      Pages 181-181
    2. Michel Marie Deza, Elena Deza
      Pages 183-195
    3. Michel Marie Deza, Elena Deza
      Pages 197-208
    4. Michel Marie Deza, Elena Deza
      Pages 209-221
    5. Michel Marie Deza, Elena Deza
      Pages 223-232
    6. Michel Marie Deza, Elena Deza
      Pages 233-245
  5. Distances in Applied Mathematics

    1. Front Matter
      Pages 247-247
    2. Michel Marie Deza, Elena Deza
      Pages 249-278
    3. Michel Marie Deza, Elena Deza
      Pages 279-290
    4. Michel Marie Deza, Elena Deza
      Pages 291-305
    5. Michel Marie Deza, Elena Deza
      Pages 307-320
  6. Computer-Related Distances

    1. Front Matter
      Pages 321-321
    2. Michel Marie Deza, Elena Deza
      Pages 323-338
    3. Michel Marie Deza, Elena Deza
      Pages 339-347
    4. Michel Marie Deza, Elena Deza
      Pages 349-369
    5. Michel Marie Deza, Elena Deza
      Pages 371-384
  7. Distances in Natural Sciences

    1. Front Matter
      Pages 385-385
    2. Michel Marie Deza, Elena Deza
      Pages 387-434
    3. Michel Marie Deza, Elena Deza
      Pages 435-464
    4. Michel Marie Deza, Elena Deza
      Pages 465-496
    5. Michel Marie Deza, Elena Deza
      Pages 497-526
  8. Real-World Distances

    1. Front Matter
      Pages 527-527
    2. Michel Marie Deza, Elena Deza
      Pages 529-543
    3. Michel Marie Deza, Elena Deza
      Pages 545-586
    4. Michel Marie Deza, Elena Deza
      Pages 587-617
  9. Back Matter
    Pages 619-650

About this book

Introduction

This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a field now regarded as an essential tool in many areas of pure and applied mathematics.

 

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