Symmetry in data mining and analysis: A unifying view based on hierarchy

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16 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)177-198
Number of pages22
JournalProceedings of the Steklov Institute of Mathematics
Volume265
Issue number1
DOIs
Publication statusPublished - Jul 2009
Externally publishedYes

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