Encyclopedia of distances

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This updated third edition of the leading reference on distance metrics features new topics from active research areas such as geometry, graph theory, probability theory, and analysis. Notable additions include polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances. The publication aligns with growing research efforts into metric spaces and distance design for various applications. Accurate metrics are increasingly vital in fields like computational biology, image analysis, speech recognition, and information retrieval. While addressing practical concerns in selecting effective distance functions, this work aims to provide the research community with a comprehensive listing of available distances. It includes standalone introductions and definitions, facilitating quick cross-referencing through bold-faced links to core entries. Additionally, the authors present intriguing curiosities in their Who’s Who of metrics, showcasing distance-related concepts that empower applied mathematicians to utilize research tools often seen as complex by non-specialists. By expanding access to these techniques and enriching the context of distances, this volume is poised to inspire new research.