title: Strict polynomial separation of two sets
metadata.name: dc.contributor.author
metadata.value: Malozemov, Vassili N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Plotkin, Artem V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-05-24T11:16:58Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-05-24T11:16:58Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Malozemov V.N., Plotkin A.V. Strict polynomial separation of two sets. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 2, pp. 232–240.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.205
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15555
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: strict linear separation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strict polynomial separation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linear programming
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: mathematical diagnostics
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Strict polynomial separation of two sets
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 232-240.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15555/1/232-240.pdf
resources.format: Adobe PDF
resources.size: 426,23 kB