From Data to the Physics Using Ultrametrics: New Results in High Dimensional Data Analysis

Fionn Murtagh

doi:10.1063/1.2193119

From Data to the Physics Using Ultrametrics: New Results in High Dimensional Data Analysis

Fionn Murtagh

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Citations (Scopus)

Abstract

We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or locally present in data. We show how the ultrametricity can be assessed in text or document collections, in time series signals, and in other areas. We conclude with a discussion of ultrametricity in astrophysics, relating to observational cosmology.

Original language	English
Title of host publication	p-ADIC Mathematical Physics
Subtitle of host publication	2nd International Conference
Editors	Andrei Yu. Khrennikov, Zoran Rakic, Igor V. Volovich
Publisher	AIP Publishing
Pages	151-161
Number of pages	11
Volume	826
Edition	1
ISBN (Print)	073540318X, 9780735403185
DOIs	https://doi.org/10.1063/1.2193119
Publication status	Published - 29 Mar 2006
Externally published	Yes
Event	2nd International Conference on p-Adic Mathematical Physics - Belgrade, Serbia Duration: 15 Sep 2005 → 21 Sep 2005 Conference number: 2 https://labs.inspirehep.net/conferences/976725

Publication series

Name	AIP Conference Proceedings
Number	1
Volume	826
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	2nd International Conference on p-Adic Mathematical Physics
Country/Territory	Serbia
City	Belgrade
Period	15/09/05 → 21/09/05
Internet address	https://labs.inspirehep.net/conferences/976725

Access to Document

10.1063/1.2193119Licence: Unspecified

Cite this

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title = "From Data to the Physics Using Ultrametrics: New Results in High Dimensional Data Analysis",

abstract = "We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or locally present in data. We show how the ultrametricity can be assessed in text or document collections, in time series signals, and in other areas. We conclude with a discussion of ultrametricity in astrophysics, relating to observational cosmology.",

keywords = "Cluster analysis, Correspondence analysis, Factor analysis, Hierarchy, Multivariate data analysis, p-adic, Phylogeny, Ultrametric",

author = "Fionn Murtagh",

year = "2006",

month = mar,

day = "29",

doi = "10.1063/1.2193119",

language = "English",

isbn = "073540318X",

volume = "826",

series = "AIP Conference Proceedings",

publisher = "AIP Publishing",

number = "1",

pages = "151--161",

editor = "Khrennikov, {Andrei Yu.} and Zoran Rakic and Volovich, {Igor V.}",

booktitle = "p-ADIC Mathematical Physics",

address = "United States",

edition = "1",

note = "2nd International Conference on p-Adic Mathematical Physics ; Conference date: 15-09-2005 Through 21-09-2005",

url = "https://labs.inspirehep.net/conferences/976725",

}

Murtagh, F 2006, From Data to the Physics Using Ultrametrics: New Results in High Dimensional Data Analysis. in AY Khrennikov, Z Rakic & IV Volovich (eds), p-ADIC Mathematical Physics: 2nd International Conference. 1 edn, vol. 826, AIP Conference Proceedings, no. 1, vol. 826, AIP Publishing, pp. 151-161, 2nd International Conference on p-Adic Mathematical Physics, Belgrade, Serbia, 15/09/05. https://doi.org/10.1063/1.2193119

From Data to the Physics Using Ultrametrics : New Results in High Dimensional Data Analysis. / Murtagh, Fionn.

p-ADIC Mathematical Physics: 2nd International Conference. ed. / Andrei Yu. Khrennikov; Zoran Rakic; Igor V. Volovich. Vol. 826 1. ed. AIP Publishing, 2006. p. 151-161 (AIP Conference Proceedings; Vol. 826, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or locally present in data. We show how the ultrametricity can be assessed in text or document collections, in time series signals, and in other areas. We conclude with a discussion of ultrametricity in astrophysics, relating to observational cosmology.

AB - We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or locally present in data. We show how the ultrametricity can be assessed in text or document collections, in time series signals, and in other areas. We conclude with a discussion of ultrametricity in astrophysics, relating to observational cosmology.

KW - Cluster analysis

KW - Correspondence analysis

KW - Factor analysis

KW - Hierarchy

KW - Multivariate data analysis

KW - p-adic

KW - Phylogeny

KW - Ultrametric

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DO - 10.1063/1.2193119

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T3 - AIP Conference Proceedings

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PB - AIP Publishing

Y2 - 15 September 2005 through 21 September 2005

ER -

From Data to the Physics Using Ultrametrics: New Results in High Dimensional Data Analysis

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