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

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Published

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

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Murtagh, F, Banks, D (ed.), House, L (ed.), McMorris, FR (ed.), Arabie, P (ed.) & Gaul, W (ed.) 2004, Thinking ultrametrically. in *Classification, Clustering, and Data Mining Applications.* Studies in Classification, Data Analysis & Knowledge Organization, Springer-Verlag, Berlin, pp. 3-14. <http://www.cs.rhul.ac.uk/home/fionn/papers/fm28.pdf>

Murtagh, F., Banks, D. (Ed.), House, L. (Ed.), McMorris, F. R. (Ed.), Arabie, P. (Ed.), & Gaul, W. (Ed.) (2004). Thinking ultrametrically. In *Classification, Clustering, and Data Mining Applications *(pp. 3-14). (Studies in Classification, Data Analysis & Knowledge Organization). Springer-Verlag. http://www.cs.rhul.ac.uk/home/fionn/papers/fm28.pdf

Murtagh F, Banks D, (ed.), House L, (ed.), McMorris FR, (ed.), Arabie P, (ed.), Gaul W, (ed.). Thinking ultrametrically. In Classification, Clustering, and Data Mining Applications. Berlin: Springer-Verlag. 2004. p. 3-14. (Studies in Classification, Data Analysis & Knowledge Organization).

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title = "Thinking ultrametrically",

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.",

keywords = "ultrametricity, ultrametric",

author = "Fionn Murtagh and D Banks and L House and McMorris, {F R} and P Arabie and W Gaul",

year = "2004",

language = "English",

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AB - 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.

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