КФУ. Карточка публикации. A Linear Separability Criterion for Sets of Euclidean Space

КАЗАНСКИЙ
ФЕДЕРАЛЬНЫЙ УНИВЕРСИТЕТ

RUS

- EN
- 中文
- ES

A LINEAR SEPARABILITY CRITERION FOR SETS OF EUCLIDEAN SPACE

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2013

Язык

английский

Авторы, сотрудники КФУ

Габидуллина Зульфия Равилевна, автор

Библиографическое описание на языке оригинала

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)

Аннотация

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

Ключевые слова

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

Название журнала

Journal of Optimization Theory and Applications

URL

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

Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку

https://repository.kpfu.ru/?p_id=148851

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Габидуллина Зульфия Равилевна	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/?p_id=148851	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	Статьи в зарубежных журналах и сборниках	ru_RU