Форма представления | Статьи в зарубежных журналах и сборниках |
Год публикации | 2013 |
Язык | английский |
|
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 |
|