Encyclopedia of distances Michel Marie Deza, Elena Deza

Format:

Book

Author/Creator:

Deza, M., 1939- author.

Deza, Elena, author.

Language:

English

Subjects (All):

Metric spaces.

Distances--Measurement.

Distances.

Genre:

Reference works

Physical Description:

1 online resource

Edition:

Second edition

Place of Publication:

Heidelberg New York Springer [2013]

Language Note:

English

System Details:

text file

PDF

Summary:

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

Contents:

Part I. Mathematics of Distances

1 General Definitions

2 Topological Spaces

3 Generalization of Metric Spaces

4 Metric Transforms

5 Metrics on Normed Structures

Part II. Geometry and Distances

6 Distances in Geometry

7 Riemannian and Hermitian Metrics

8 Distances on Surfaces and Knots

9 Distances on Convex Bodies, Cones and Simplicial Complexes

Part III. Distances in Classical Mathematics

10 Distances in Algebra

11 Distances on Strings and Permutations

12 Distances on Numbers, Polynominals and Matrices

13 Distances in Functional Analysis

14 Distances in Probability Theory

Part IV. Distances in Applied Mathematics

15 Distances in Graph theory

16 Distances in Coding Theory

17 Distances and Similarities in Data Analysis

18 Distances in Systems and Mathematical Engineering

Part V. Computer-Related Distances

19 Distances on Real and Digital Planes

20 Voronoi Diagram Distances

21 Image and Audio Distances

22 Distances in Networks

Part VI. Distances in Natural Sciences

23 Distances in Biology

24 Distances in Physics and Chemistry

25 Distances in Earth Science and Astronomy

26 Distances in Cosmology and Theory of Relativity

Part VII. Real-World Distances

27 Length Measures and Scales

28 Distances in Applied Social Sciences

29 Other Distances

Notes:

Includes bibliographical references (pages 619-625) and index

Print version record

Other Format:

Print version Deza, M., 1939- Encyclopedia of distances.

ISBN:

9783642309588

3642309585

9781283910958

1283910950

OCLC:

889208911

Access Restriction:

Restricted for use by site license