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In this paper we aim to use different metrics in the Euclidean space andSobolev type metrics in function spaces in order to produce reliable parametersfor the differentiation of point distributions and dynamical systems. The maintool is the analysis of the geometrical evolution of the hypergraphs generatedby the growth of the radial parameters for a choice of an appropriate metric inthe space containing the data points. Once this geometric dynamics is obtainedwe use Lebesque and Sobolev type norms in order to compare the basic geometricsignals obtained.

Data analysis and the metric evolution of hypergraphs