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Encyclopedia of Distances

  • Michel Marie Deza
  • Elena Deza

Table of contents

  1. Front Matter
    Pages i-xxii
  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 71-85
    5. Michel Marie Deza, Elena Deza
      Pages 87-96
    6. Michel Marie Deza, Elena Deza
      Pages 97-108
  3. Geometry and Distances

    1. Front Matter
      Pages 109-109
    2. Michel Marie Deza, Elena Deza
      Pages 111-133
    3. Michel Marie Deza, Elena Deza
      Pages 135-168
    4. Michel Marie Deza, Elena Deza
      Pages 169-182
    5. Michel Marie Deza, Elena Deza
      Pages 183-195
  4. Distances in Classical Mathematics

    1. Front Matter
      Pages 197-197
    2. Michel Marie Deza, Elena Deza
      Pages 199-214
    3. Michel Marie Deza, Elena Deza
      Pages 215-228
    4. Michel Marie Deza, Elena Deza
      Pages 229-246
    5. Michel Marie Deza, Elena Deza
      Pages 247-257
    6. Michel Marie Deza, Elena Deza
      Pages 259-274
  5. Distances in Applied Mathematics

    1. Front Matter
      Pages 275-275
    2. Michel Marie Deza, Elena Deza
      Pages 277-311
    3. Michel Marie Deza, Elena Deza
      Pages 313-325
    4. Michel Marie Deza, Elena Deza
      Pages 327-345
    5. Michel Marie Deza, Elena Deza
      Pages 347-362
  6. Computer-Related Distances

    1. Front Matter
      Pages 363-363
    2. Michel Marie Deza, Elena Deza
      Pages 365-381
    3. Michel Marie Deza, Elena Deza
      Pages 383-392
    4. Michel Marie Deza, Elena Deza
      Pages 393-418
    5. Michel Marie Deza, Elena Deza
      Pages 419-435
  7. Distances in Natural Sciences

    1. Front Matter
      Pages 437-437
    2. Michel Marie Deza, Elena Deza
      Pages 439-497
    3. Michel Marie Deza, Elena Deza
      Pages 499-531
    4. Michel Marie Deza, Elena Deza
      Pages 533-575
    5. Michel Marie Deza, Elena Deza
      Pages 577-609
  8. Real-World Distances

    1. Front Matter
      Pages 611-611
    2. Michel Marie Deza, Elena Deza
      Pages 613-627
    3. Michel Marie Deza, Elena Deza
      Pages 629-682
    4. Michel Marie Deza, Elena Deza
      Pages 683-722
  9. Back Matter
    Pages 723-756

About this book

Introduction

This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis.

New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric, algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja distance, spectral semimetric between graphs, channel metrization, and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics, including: dynamic time wrapping distance, memory distance, allometry, atmospheric depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of units, and walkability distance.

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 generalized distances dynamic time wrapping distance

Authors and affiliations

  • Michel Marie Deza
    • 1
  • Elena Deza
    • 2
  1. 1.Ecole Normale SupérieureParisFrance
  2. 2.Moscow State Pedagogical UniversityMoscowRussia

Bibliographic information