A geometric approach to the problem of reconstruction of the sample behavior in hidden dimensions

Authors:
A. Vinogradov;Yu. Laptin
Affiliations:
Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, Russia 119333;Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine 03680
Venue:
Pattern Recognition and Image Analysis
Year:
2010

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Abstract

We investigate a direct geometric approach to the problem of reconstruction of the behavior of a sample of hidden dimensions. A method for an improved description of cluster sampling, based on the interpretation of nonlinearities in the empirical distribution of both local projections of a uniform distribution on a smooth manifold, defined in the hidden dimension, is given. This method can be used to resolve a number of critical features in the empirical distributions. The a priori assumptions under which many variants of reconstruction of sampling behavior in the hidden dimensions are limited are considered.