Encyclopedia of 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.

From the reviews:

"Michel Marie Deza and Elena Deza’s Encyclopedia of Distances is exactly what it says, it is – an encyclopedia of topics that relate to measuring distance. … It is a truly original compilation of material, one that almost anyone with some mathematical experience might enjoy browsing." (Bill Wood, The Mathematical Association of America, September, 2009)

“Encyclopedia of Distances is a revision of the earlier Dictionary of Distances (2006). … Toward the end of the encyclopedia several chapters address the definition of distances in other areas of the sciences including astronomy, biology, geography, relativity, and even some of the social sciences. Non-mathematicians will find these chapters more approachable … . This volume is suitable … for institutions with graduate programs in mathematics. Summing Up: Recommended. Graduate students through professionals/practitioners.” (J. O. Christensen, Choice, Vol. 47 (5), January, 2010)

“It does, though, contain an interesting collection of articles; mainly related to distances used in maths … . Its main audience is researchers who are interested in an aspect of distance and its measurement. … Each definition clearly identifies where it is building on other definitions in the book so the reader can refer to those entries as well. Overall, this is a specialist reference book … . For those who are already knowledgeable in this subject then it would be an interesting review … .” (Clari Gosling, Reference Reviews, Vol. 24 (6), 2010)

“In this book a collection of more than 1,000 distances and metrics is presented coming from nearly every part of pure and applied mathematics, of natural sciences and of every day life as well. … Often informative comments are added, which make this book an even more valuable source of reference.” (G. Kowol, Monatshefte für Mathematik, Vol. 160 (1), April, 2010)