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