Encyclopedia of distances
M. Deza (Author), Elena Deza (Author)
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
xviii, 650 pages : illustrations ; 24 cm
9783642309571, 9783642309588, 3642309577, 3642309585
953361409
1 General Definitions
2 Topological Spaces
3 Generalization of Metric Spaces
4 Metric Transforms
5 Metrics on Normed Structures
6 Distances in Geometry
7 Riemannian and Hermitian Metrics
8 Distances on Surfaces and Knots
9 Distances on Convex Bodies, Cones and Simplicial Complexes
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
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
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
27 Length Measures and Scales
28 Distances in Applied Social Sciences
29 Other Distances