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

TitleResearch of nonparametric maximum-depth classifiers based on the spatial quantiles
Publication TypeJournal Article
Year of Publication2015
AuthorsGalkin, OA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.10.021
Issue10
SectionInformation Science and Cybernetics
Pagination21-26
Date Published10/2015
LanguageUkrainian
Abstract

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.
KeywordsBayes risk, spatial depth, spatial quantiles
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