TY - JOUR
T1 - Symmetry in data mining and analysis
T2 - A unifying view based on hierarchy
AU - Murtagh, Fionn
PY - 2009/7
Y1 - 2009/7
N2 - 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.
AB - 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.
KW - steklov institute
KW - terminal node
KW - wreath product
KW - haar wavelet
KW - symbol sequence
UR - http://www.scopus.com/inward/record.url?scp=70350073872&partnerID=8YFLogxK
U2 - 10.1134/S0081543809020175
DO - 10.1134/S0081543809020175
M3 - Article
AN - SCOPUS:70350073872
VL - 265
SP - 177
EP - 198
JO - Proceedings of the Steklov Institute of Mathematics
JF - Proceedings of the Steklov Institute of Mathematics
SN - 0081-5438
IS - 1
ER -