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

1Galkin, OA
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 2:25-30
Section: Information Science and Cybernetics
Language: Ukrainian

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.

Keywords: depth-based classifier, nonparametric consistency, symmetrization
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