An integer programming approach for the 2-class single-group classification problem

Autores
Corrêa, Ricardo C.; Blaum, Manuela; Marenco, Javier Leonardo; Koch, Ivo Valerio; Mydlarz, Marcelo
Año de publicación
2019
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
Two sets XB, XR ⊆ Rd are linearly separable if their convex hulls are disjoint, implying that a hyperplane separating XB from XR exists. Such a hyperplane provides a method for classifying new points, according to the side of the hyperplane in which the new points lie. In this work we consider a particular case of the 2-class classification problem, which asks to select the maximum number of points from XB and XR in such a way that the selected points are linearly separable. We present an integer programming formulation for this problem, explore valid inequalities for the associated polytope, and develop a cutting plane approach coupled with a lazy-constraints scheme.
Fil: Corrêa, Ricardo C.. Universidade Federal Rural Do Rio de Janeiro; Brasil
Fil: Blaum, Manuela. Universidad Nacional de General Sarmiento; Argentina
Fil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento; Argentina
Fil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; Argentina
Fil: Mydlarz, Marcelo. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)
Belo Horizonte
Brasil
Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior
Conselho Nacional de Desenvolvimento Científico e Técnologico do Brasil
Universidade Federal de Minas Gerais
Materia
Classification
Integer programming
Polyhedral combinatorics
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/129571
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/129571
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An integer programming approach for the 2-class single-group classification problemCorrêa, Ricardo C.Blaum, ManuelaMarenco, Javier LeonardoKoch, Ivo ValerioMydlarz, MarceloClassificationInteger programmingPolyhedral combinatoricshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Two sets XB, XR ⊆ Rd are linearly separable if their convex hulls are disjoint, implying that a hyperplane separating XB from XR exists. Such a hyperplane provides a method for classifying new points, according to the side of the hyperplane in which the new points lie. In this work we consider a particular case of the 2-class classification problem, which asks to select the maximum number of points from XB and XR in such a way that the selected points are linearly separable. We present an integer programming formulation for this problem, explore valid inequalities for the associated polytope, and develop a cutting plane approach coupled with a lazy-constraints scheme.Fil: Corrêa, Ricardo C.. Universidade Federal Rural Do Rio de Janeiro; BrasilFil: Blaum, Manuela. Universidad Nacional de General Sarmiento; ArgentinaFil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento; ArgentinaFil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; ArgentinaFil: Mydlarz, Marcelo. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaLatin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)Belo HorizonteBrasilCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorConselho Nacional de Desenvolvimento Científico e Técnologico do BrasilUniversidade Federal de Minas GeraisElsevier2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectSimposioJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/129571An integer programming approach for the 2-class single-group classification problem; Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2019); Belo Horizonte; Brasil; 2019; 321-3311571-0661CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1571066119300799info:eu-repo/semantics/altIdentifier/doi/10.1016/j.entcs.2019.08.029Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:22:40Zoai:ri.conicet.gov.ar:11336/129571instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:22:40.852CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An integer programming approach for the 2-class single-group classification problem
title An integer programming approach for the 2-class single-group classification problem
spellingShingle An integer programming approach for the 2-class single-group classification problem
Corrêa, Ricardo C.
Classification
Integer programming
Polyhedral combinatorics
title_short An integer programming approach for the 2-class single-group classification problem
title_full An integer programming approach for the 2-class single-group classification problem
title_fullStr An integer programming approach for the 2-class single-group classification problem
title_full_unstemmed An integer programming approach for the 2-class single-group classification problem
title_sort An integer programming approach for the 2-class single-group classification problem
dc.creator.none.fl_str_mv Corrêa, Ricardo C.
Blaum, Manuela
Marenco, Javier Leonardo
Koch, Ivo Valerio
Mydlarz, Marcelo
author Corrêa, Ricardo C.
author_facet Corrêa, Ricardo C.
Blaum, Manuela
Marenco, Javier Leonardo
Koch, Ivo Valerio
Mydlarz, Marcelo
author_role author
author2 Blaum, Manuela
Marenco, Javier Leonardo
Koch, Ivo Valerio
Mydlarz, Marcelo
author2_role author
author
author
author
dc.subject.none.fl_str_mv Classification
Integer programming
Polyhedral combinatorics
topic Classification
Integer programming
Polyhedral combinatorics
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Two sets XB, XR ⊆ Rd are linearly separable if their convex hulls are disjoint, implying that a hyperplane separating XB from XR exists. Such a hyperplane provides a method for classifying new points, according to the side of the hyperplane in which the new points lie. In this work we consider a particular case of the 2-class classification problem, which asks to select the maximum number of points from XB and XR in such a way that the selected points are linearly separable. We present an integer programming formulation for this problem, explore valid inequalities for the associated polytope, and develop a cutting plane approach coupled with a lazy-constraints scheme.
Fil: Corrêa, Ricardo C.. Universidade Federal Rural Do Rio de Janeiro; Brasil
Fil: Blaum, Manuela. Universidad Nacional de General Sarmiento; Argentina
Fil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento; Argentina
Fil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; Argentina
Fil: Mydlarz, Marcelo. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)
Belo Horizonte
Brasil
Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior
Conselho Nacional de Desenvolvimento Científico e Técnologico do Brasil
Universidade Federal de Minas Gerais
description Two sets XB, XR ⊆ Rd are linearly separable if their convex hulls are disjoint, implying that a hyperplane separating XB from XR exists. Such a hyperplane provides a method for classifying new points, according to the side of the hyperplane in which the new points lie. In this work we consider a particular case of the 2-class classification problem, which asks to select the maximum number of points from XB and XR in such a way that the selected points are linearly separable. We present an integer programming formulation for this problem, explore valid inequalities for the associated polytope, and develop a cutting plane approach coupled with a lazy-constraints scheme.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Simposio
Journal
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/129571
An integer programming approach for the 2-class single-group classification problem; Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2019); Belo Horizonte; Brasil; 2019; 321-331
1571-0661
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129571
identifier_str_mv An integer programming approach for the 2-class single-group classification problem; Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2019); Belo Horizonte; Brasil; 2019; 321-331
1571-0661
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1571066119300799
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.entcs.2019.08.029
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.coverage.none.fl_str_mv Internacional
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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