Thinking ultrametrically. / Murtagh, Fionn; Banks, D (Editor); House, L (Editor); McMorris, F R (Editor); Arabie, P (Editor); Gaul, W (Editor).

Classification, Clustering, and Data Mining Applications. Berlin : Springer-Verlag, 2004. p. 3-14 (Studies in Classification, Data Analysis & Knowledge Organization).

Research output: Chapter in Book/Report/Conference proceedingChapter

Published
  • Fionn Murtagh
  • D Banks (Editor)
  • L House (Editor)
  • F R McMorris (Editor)
  • P Arabie (Editor)
  • W Gaul (Editor)

Abstract

The triangular inequality is a defining property of a metric space, while the stronger ultrametric inequality is a defining property of an ultrametric space. Ultrametric distance is defined from p-adic valuation. It is known that ultrametricity is a natural property of spaces that are sparse. Here we look at the quantification of ultrametricity. We also look at data compression based on a new ultrametric wavelet transform. We conclude with computational implications of prevalent and perhaps ubiquitous ultrametricity.
Original languageEnglish
Title of host publicationClassification, Clustering, and Data Mining Applications
Place of PublicationBerlin
PublisherSpringer-Verlag
Pages3-14
ISBN (Print)3540220143
Publication statusPublished - 2004

Publication series

NameStudies in Classification, Data Analysis & Knowledge Organization
PublisherSpringer-Verlag
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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