Thinking ultrametrically

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

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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

Keywords

  • ultrametricity
  • ultrametric

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