Строгое полиномиальное отделение двух множеств

Research output

Abstract

One of the main tasks of mathematical diagnostics is the strict separation of two finite sets in Euclidean space. A strict linear separation is widely known and is reduced to a linear programming problem. We introduce a strict polynomial separation and show that the strict polynomial separation of two sets also is reduced to a linear programming problem. The objective function of the linear programming problem proposed in this paper has the following feature: its optimal value can only be zero or one. It is zero if the sets are strictly polynomially separable; otherwise, it is one. We give illustrative examples of strict separation of two sets with the help of two-variable fourth-degree algebraic polynomials on the plane. We also analyze the efficiency of applying the strict polynomial separation to binary classification problems.
Translated title of the contributionStrict polynomial separation of two sets
Original languageRussian
Pages (from-to)232-240
JournalВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ
Volume6(64)
Issue number2
DOIs
Publication statusPublished - 2019

Scopus subject areas

  • Mathematics(all)

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