Thinking ultrametrically

Fionn Murtagh; D Banks; L House; F R McMorris; P Arabie; W Gaul

Thinking ultrametrically

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

Department of Computer Science

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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 language	English
Title of host publication	Classification, Clustering, and Data Mining Applications
Place of Publication	Berlin
Publisher	Springer-Verlag
Pages	3-14
ISBN (Print)	3540220143
Publication status	Published - 2004

Publication series

Name	Studies in Classification, Data Analysis & Knowledge Organization
Publisher	Springer-Verlag

Keywords

ultrametricity
ultrametric

Access to Document

Full Text

http://www.cs.rhul.ac.uk/home/fionn/papers/fm28.pdf

Cite this

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