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

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


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
ISBN (Print)3540220143
Publication statusPublished - 2004

Publication series

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

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