Geodesic
Symmetry in Data Mining and Analysis: A~Unifying View Based on Hierarchy
Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 189-210

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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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     author = {F. Murtagh},
     title = {Symmetry in {Data} {Mining} and {Analysis:} {A~Unifying} {View} {Based} on {Hierarchy}},
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F. Murtagh. Symmetry in Data Mining and Analysis: A~Unifying View Based on Hierarchy. Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 189-210. http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a16/