Standard

Strict Polynomial Separation of Two Sets. / Malozemov, V. N. ; Plotkin, A. V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 52, No. 2, 2019, p. 162-168.

Research output: Contribution to journal › Article › peer-review

Harvard

Malozemov, VN & Plotkin, AV 2019, 'Strict Polynomial Separation of Two Sets', Vestnik St. Petersburg University: Mathematics, vol. 52, no. 2, pp. 162-168. https://doi.org/10.3103/S1063454119020109

APA

Malozemov, V. N., & Plotkin, A. V. (2019). Strict Polynomial Separation of Two Sets. Vestnik St. Petersburg University: Mathematics, 52(2), 162-168. https://doi.org/10.3103/S1063454119020109

Vancouver

Malozemov VN, Plotkin AV. Strict Polynomial Separation of Two Sets. Vestnik St. Petersburg University: Mathematics. 2019;52(2):162-168. https://doi.org/10.3103/S1063454119020109

Author

Malozemov, V. N. ; Plotkin, A. V. / Strict Polynomial Separation of Two Sets. In: Vestnik St. Petersburg University: Mathematics. 2019 ; Vol. 52, No. 2. pp. 162-168.

BibTeX

@article{ac816d1215b149229a8bb53d35ddf688,
title = "Strict Polynomial Separation of Two Sets",
abstract = "One of the main tasks of mathematical diagnostics is the strict separation of two finite sets in a Euclidean space. Strict linear separation is widely known and reduced to the solution of a linear programming problem. We introduce the notion of strict polynomial separation and show that the strict polynomial separation of two sets can be also reduced to the solution of a linear programming problem. The objective function of the linear programming problem proposed in this paper has the following feature: its optimal value can be only zero or one, i.e., it is zero if the sets admit strict polynomial separation and one otherwise. Some illustrative examples of the strict separation of two sets on a plane with the use of fourth degree algebraic polynomials in two variables are given. The application efficiency of strict polynomial separation to binary data classification problems is analyzed.",
keywords = "linear programming, mathematical diagnostics, strict linear separation, strict polynomial separation",
author = "Malozemov, {V. N.} and Plotkin, {A. V.}",
note = "Malozemov, V.N. & Plotkin, A.V. Vestnik St.Petersb. Univ.Math. (2019) 52: 162. https://doi.org/10.1134/S1063454119020109",
year = "2019",
doi = "10.3103/S1063454119020109",
language = "English",
volume = "52",
pages = "162--168",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Strict Polynomial Separation of Two Sets

AU - Malozemov, V. N.

AU - Plotkin, A. V.

N1 - Malozemov, V.N. & Plotkin, A.V. Vestnik St.Petersb. Univ.Math. (2019) 52: 162. https://doi.org/10.1134/S1063454119020109

PY - 2019

Y1 - 2019

N2 - One of the main tasks of mathematical diagnostics is the strict separation of two finite sets in a Euclidean space. Strict linear separation is widely known and reduced to the solution of a linear programming problem. We introduce the notion of strict polynomial separation and show that the strict polynomial separation of two sets can be also reduced to the solution of a linear programming problem. The objective function of the linear programming problem proposed in this paper has the following feature: its optimal value can be only zero or one, i.e., it is zero if the sets admit strict polynomial separation and one otherwise. Some illustrative examples of the strict separation of two sets on a plane with the use of fourth degree algebraic polynomials in two variables are given. The application efficiency of strict polynomial separation to binary data classification problems is analyzed.

AB - One of the main tasks of mathematical diagnostics is the strict separation of two finite sets in a Euclidean space. Strict linear separation is widely known and reduced to the solution of a linear programming problem. We introduce the notion of strict polynomial separation and show that the strict polynomial separation of two sets can be also reduced to the solution of a linear programming problem. The objective function of the linear programming problem proposed in this paper has the following feature: its optimal value can be only zero or one, i.e., it is zero if the sets admit strict polynomial separation and one otherwise. Some illustrative examples of the strict separation of two sets on a plane with the use of fourth degree algebraic polynomials in two variables are given. The application efficiency of strict polynomial separation to binary data classification problems is analyzed.

KW - linear programming

KW - mathematical diagnostics

KW - strict linear separation

KW - strict polynomial separation

UR - http://www.scopus.com/inward/record.url?scp=85067201094&partnerID=8YFLogxK

U2 - 10.3103/S1063454119020109

DO - 10.3103/S1063454119020109

M3 - Article

VL - 52

SP - 162

EP - 168

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 43117367