Deza M.M., Deza E. Encyclopedia of Distances

Springer, 2012. — 668 p. — 2nd ed. — ISBN: 3642309577,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.Mathematics of Distances
General Definitions
Topological Spaces
Generalizations of Metric Spaces
Metric Transforms
Metrics on Normed Structures
Geometry and Distances
Distances in Geometry
Riemannian and Hermitian Metrics
Distances on Surfaces and Knots
Distances on Convex Bodies, Cones, and Simplicial Complexes
Distances in Classical Mathematics
Distances in Algebra
Distances on Strings and Permutations
Distances on Numbers, Polynomials, and Matrices
Distances in Functional Analysis
Distances in Probability Theory
Distances in Applied Mathematics
Distances in Graph Theory
Distances in Coding Theory
Distances and Similarities in Data Analysis
Distances in Systems and Mathematical Engineering
Computer-Related Distances
Distances on Real and Digital Planes
Voronoi Diagram Distances
Image and Audio Distances
Distances in Networks
Distances in Natural Sciences
Distances in Biology
Distances in Physics and Chemistry
Distances in Earth Science and Astronomy
Distances in Cosmology and Theory of Relativity
Real-World Distances
Length Measures and Scales
Distances in Applied Social Sciences
Other Distances
References
Index