Encyclopedia of Distances [electronic resource] /
Deza, Michel Marie.author.
Deza, Elena.author.
Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just as research intensifies into metric spaces and especially, distance design for applications. These distances are particularly crucial, for example, in computational biology, image analysis, speech recognition, and information retrieval. Here, an assessment of the practical questions arising during selection of a "good'' distance function has been left aside in favor of a comprehensive listing of the main available distances, a useful tool for the distance design community. This reader-friendly reference offers both independent introductions and definitions, while at the same time making cross-referencing easy through hyperlink-like boldfaced references to original definitions. This high-quality publication is a mix of reference resource and coffee-table book. A number of fascinating curiosities appear in this ‘Who’s Who' of distances. Besides distances themselves, the authors have collected many distance-related notions and paradigms, giving applied mathematicians in other sectors easy access to those research tools that are arcane for non-specialists. What’s more, they come in ready-to-use fashion. This, as well as the appearance of some distances in different contexts, will be a stimulus to new research.
Description based upon print version of record.
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 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 Internet and Similar Networks -- Part VI. Distances in Natural Sciences -- 23 Distances in Biology -- 24 Distances in Physics and Chemistry -- 25 Distances in Geography, Geophysics 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.
Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just as research intensifies into metric spaces and especially, distance design for applications. These distances are particularly crucial, for example, in computational biology, image analysis, speech recognition, and information retrieval. Here, an assessment of the practical questions arising during selection of a "good'' distance function has been left aside in favor of a comprehensive listing of the main available distances, a useful tool for the distance design community. This reader-friendly reference offers both independent introductions and definitions, while at the same time making cross-referencing easy through hyperlink-like boldfaced references to original definitions. This high-quality publication is a mix of reference resource and coffee-table book. A number of fascinating curiosities appear in this ‘Who’s Who' of distances. Besides distances themselves, the authors have collected many distance-related notions and paradigms, giving applied mathematicians in other sectors easy access to those research tools that are arcane for non-specialists. What’s more, they come in ready-to-use fashion. This, as well as the appearance of some distances in different contexts, will be a stimulus to new research.
Discrete mathematics.
Differential geometry.
Topology.
Geometry.
Computer mathematics.
Mathematics.
Visualization.
Discrete Mathematics.
Differential Geometry.
Topology.
Geometry.
Computational Mathematics and Numerical Analysis.
Visualization.