KFU. Card publication. A Linear Separability Criterion for Sets of Euclidean Space

KAZAN
FEDERAL UNIVERSITY

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- 中文
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A LINEAR SEPARABILITY CRITERION FOR SETS OF EUCLIDEAN SPACE

Form of presentation

Articles in international journals and collections

Year of publication

2013

Язык

английский

Authors, employees of KFU

Gabidullina Zulfiya Ravilevna, author

Bibliographic description in the original language

Gabidullina Z.R., A Linear Separability Criterion for Sets of Euclidean Space//Journal of Optimization Theory and Applications. - 2013. - Vol.158, Is.1. - P.145-171. (WOS)

Annotation

We prove new theorems which describe a necessary and sufficient condition for linear (strong and non-strong) separability and inseparability of the sets in a finite-dimensional Euclidean space. We propose a universal measure for the thickness of geometric margin (both the strong separation margin (separator) and the margin of unseparated points (pseudo-separator)) formed between parallel generalized supporting hyperplanes of two sets which are separated. The introduced measure permits one to compare results of linear separation obtained by different techniques for both disjoint and linearly inseparable sets. The optimization program the formulation of which provides for the separable sets a maximum thickness of the separator is considered. When the sets are inseparable, the same solver is guaranteed to construct a pseudo-separator with a minimum thickness. We estimate the distance between the convex closed sets. We construct a cone of generalized support vectors for hyperplanes each

Keywords

cone of support vectors, distance between the sets, separator, pseudo-separator, thickness of the separator (pseudo-separator), generalized supporting hyperplane, generalized support vector, projection

The name of the journal

Journal of Optimization Theory and Applications

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84878795454&partnerID=40&md5=042317a492d6982d1ec3ea8212359a11

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=148851&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Gabidullina Zulfiya Ravilevna	ru_RU
dc.date.accessioned	2013-01-01T00:00:00Z	ru_RU
dc.date.available	2013-01-01T00:00:00Z	ru_RU
dc.date.issued	2013	ru_RU
dc.identifier.citation	Gabidullina Z.R., A Linear Separability Criterion for Sets of Euclidean Space//Journal of Optimization Theory and Applications. - 2013. - Vol.158, Is.1. - P.145-171. (WOS)	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=148851&p_lang=2	ru_RU
dc.description.abstract	Journal of Optimization Theory and Applications	ru_RU
dc.description.abstract	We prove new theorems which describe a necessary and sufficient condition for linear (strong and non-strong) separability and inseparability of the sets in a finite-dimensional Euclidean space. We propose a universal measure for the thickness of geometric margin (both the strong separation margin (separator) and the margin of unseparated points (pseudo-separator)) formed between parallel generalized supporting hyperplanes of two sets which are separated. The introduced measure permits one to compare results of linear separation obtained by different techniques for both disjoint and linearly inseparable sets. The optimization program the formulation of which provides for the separable sets a maximum thickness of the separator is considered. When the sets are inseparable, the same solver is guaranteed to construct a pseudo-separator with a minimum thickness. We estimate the distance between the convex closed sets. We construct a cone of generalized support vectors for hyperplanes each	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	cone of support vectors	ru_RU
dc.subject	distance between the sets	ru_RU
dc.subject	separator	ru_RU
dc.subject	pseudo-separator	ru_RU
dc.subject	thickness of the separator (pseudo-separator)	ru_RU
dc.subject	generalized supporting hyperplane	ru_RU
dc.subject	generalized support vector	ru_RU
dc.subject	projection	ru_RU
dc.title	A Linear Separability Criterion for Sets of Euclidean Space	ru_RU
dc.type	Articles in international journals and collections	ru_RU