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Solving the Classification Problem Using ε-nets

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Cybernetics and Systems Analysis Aims and scope

Abstract

We propose a new method to solve the classification problem based on separation of two sets in space Rd by constructing and separating their ε-nets in a range space with respect to hyperplanes. The concept of separation domain is introduced as the set of possible values of ε for which the sets can be separated. The paper contains examples of separation domain for random variables with different distributions and proves the theorem about its convergence. The concept of the set of all possible ε-nets of some set is introduced and its properties are proved. The weak convergence of the normalized difference of empirical and theoretical separation curves to the normal distribution is proved. It makes it possible to check the hypothesis about the place of theoretical separation curve at a specific point.

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Authors and Affiliations

  1. Bukovinian State Medical Uniersity, Chernivtsi, Ukraine

    M. A. Ivanchuk

  2. Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine

    I. V. Malyk

Authors
  1. M. A. Ivanchuk
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  2. I. V. Malyk
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Correspondence to M. A. Ivanchuk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2016, pp. 134–144.

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Ivanchuk, M.A., Malyk, I.V. Solving the Classification Problem Using ε-nets. Cybern Syst Anal 52, 613–622 (2016). https://doi.org/10.1007/s10559-016-9863-9

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  • DOI: https://doi.org/10.1007/s10559-016-9863-9

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