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

This article is cited in 6 scientific papers (total in 6 papers)

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.

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

Bibliographic databases:

UDC: 519.72
Received in January 2009

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
\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
\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 265
\pages 177--198

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    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  crossref  mathscinet  zmath  isi  scopus
    2. Murtagh F., Contreras P., “Algorithms for Hierarchical Clustering: an Overview”, Wiley Interdiscip. Rev.-Data Mining Knowl. Discov., 2:1 (2012), 86–97  crossref  mathscinet  isi  scopus
    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  zmath  isi
    4. Kane J., Naumov P., “Symmetry in Information Flow”, Ann. Pure Appl. Log., 165:1, SI (2014), 253–265  crossref  mathscinet  zmath  isi  scopus
    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  crossref  isi  scopus
    6. Muntean M., Brandas C., Cirstea T., “Framework For a Symmetric Integration Approach”, Symmetry-Basel, 11:2 (2019), 224  crossref  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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