Research of nonparametric maximum-depth classifiers based on the spatial quantiles

1Galkin, OA
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2015, 10:21-26
Section: Information Science and Cybernetics
Language: Ukrainian

A nonparametric approach is proposed to solve the recognition problems, when separating surfaces cannot effectively be approximated by finite-parametric linear or quadratic functions. The approach is based on a function of the spatial depth, which is computationally less expensive and can be used for pattern recognition problems in an infinite-dimensional Hilbert space. A depth-based classifier is built on the basis of the concept of spatial quantiles. The properties of optimality are investigated in the case where the a posteriori probabilities of competing elliptical sets are equal. The uniform convergence of the spatial depth function is studied, and the estimates of the effectiveness of maximum depth classifiers are calculated.

Keywords: Bayes risk, spatial depth, spatial quantiles
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