Affine-invariant depth-based classifiers on the basis of the k-nearest neighbors method

TitleAffine-invariant depth-based classifiers on the basis of the k-nearest neighbors method
Publication TypeJournal Article
Year of Publication2016
AuthorsGalkin, OA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.02.025
Issue2
SectionInformation Science and Cybernetics
Pagination25-30
Date Published2/2016
LanguageUkrainian
Abstract

Depth-based classifiers on the basis of the k-nearest neighbors method are studied with nonparametric consistency for any continuous distribution. The method of symmetrization of a depth function is proposed, providing a centrally external ordering to determine the nearest neighbors. The construction of a symmetrization asymptotically guarantees the uniqueness of the deepest point that solves the problem of a convex domain with an infinite set of the deepest points. The constructed depth-based classifier based on the depth-based neighborhoods is affine invariant and, therefore, insensitive to extreme values.

Keywordsdepth-based classifier, nonparametric consistency, symmetrization
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