RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2009, Volume 265, Pages 189–210 (Mi tm834)

Symmetry in Data Mining and Analysis: A Unifying View Based on Hierarchy

F. Murtaghab

a Science Foundation Ireland, Dublin, Ireland
b Department of Computer Science, University of London, Egham, UK

Abstract: Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational, or otherwise empirical, domain of interest. “Structure” has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Symmetries directly point to invariants that pinpoint intrinsic properties of the data and of the background empirical domain of interest. As our data models change, so too do our perspectives on analyzing data. The structures in data surveyed here are based on hierarchy, represented as $p$-adic numbers or an ultrametric topology.

Full text: PDF file (278 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 265, 177–198

Bibliographic databases:

UDC: 519.72
Language:

Citation: F. Murtagh, “Symmetry in Data Mining and Analysis: A Unifying View Based on Hierarchy”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Tr. Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 189–210; Proc. Steklov Inst. Math., 265 (2009), 177–198

Citation in format AMSBIB
\Bibitem{Mur09} \by F.~Murtagh \paper Symmetry in Data Mining and Analysis: A~Unifying View Based on Hierarchy \inbook Selected topics of mathematical physics and $p$-adic analysis \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2009 \vol 265 \pages 189--210 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm834} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2599554} \zmath{https://zbmath.org/?q=an:1185.68277} \elib{https://elibrary.ru/item.asp?id=12601461} \transl \jour Proc. Steklov Inst. Math. \yr 2009 \vol 265 \pages 177--198 \crossref{https://doi.org/10.1134/S0081543809020175} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000268514300017} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350073872} 

• http://mi.mathnet.ru/eng/tm834
• http://mi.mathnet.ru/eng/tm/v265/p189

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Contreras P., Murtagh F., “Fast, Linear Time Hierarchical Clustering Using the Baire Metric”, J. Classif., 29:2 (2012), 118–143
2. Murtagh F., Contreras P., “Algorithms for Hierarchical Clustering: an Overview”, Wiley Interdiscip. Rev.-Data Mining Knowl. Discov., 2:1 (2012), 86–97
3. Kane J., Naumov P., “Symmetries and Epistemic Reasoning”, Computational Logic in Multi-Agent Systems, Clima XIV, Lecture Notes in Artificial Intelligence, 8143, eds. Leite J., Son T., Torroni P., VanDerTorre L., Woltran S., Springer-Verlag Berlin, 2013, 190–205
4. Kane J., Naumov P., “Symmetry in Information Flow”, Ann. Pure Appl. Log., 165:1, SI (2014), 253–265
5. Murtagh F., “Big Data Scaling Through Metric Mapping: Exploiting the Remarkable Simplicity of Very High Dimensional Spaces Using Correspondence Analysis”, Data Science: Innovative Developments in Data Analysis and Clustering, Studies in Classification Data Analysis and Knowledge Organization, eds. Palumbo F., Montanari A., Vichi M., Springer International Publishing Ag, 2017, 295–306
6. Muntean M., Brandas C., Cirstea T., “Framework For a Symmetric Integration Approach”, Symmetry-Basel, 11:2 (2019), 224
•  Number of views: This page: 273 Full text: 41 References: 42