A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering

Detalhes bibliográficos
Autor(a) principal: Aloise,Daniel
Data de Publicação: 2009
Outros Autores: Hansen,Pierre
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000300002
Resumo: Minimum sum-of-squares clustering (MSSC) consists in partitioning a given set of n points into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. Recently, Peng & Xia (2005) established the equivalence between 0-1 semidefinite programming (SDP) and MSSC. In this paper, we propose a branch-and-cut algorithm for the underlying 0-1 SDP model. The algorithm obtains exact solutions for fairly large data sets with computing times comparable with those of the best exact method found in the literature.
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spelling A branch-and-cut SDP-based algorithm for minimum sum-of-squares clusteringclusteringsum-of-squaressemidefinite programmingMinimum sum-of-squares clustering (MSSC) consists in partitioning a given set of n points into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. Recently, Peng & Xia (2005) established the equivalence between 0-1 semidefinite programming (SDP) and MSSC. In this paper, we propose a branch-and-cut algorithm for the underlying 0-1 SDP model. The algorithm obtains exact solutions for fairly large data sets with computing times comparable with those of the best exact method found in the literature.Sociedade Brasileira de Pesquisa Operacional2009-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000300002Pesquisa Operacional v.29 n.3 2009reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/S0101-74382009000300002info:eu-repo/semantics/openAccessAloise,DanielHansen,Pierreeng2010-02-03T00:00:00Zoai:scielo:S0101-74382009000300002Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2010-02-03T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
title A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
spellingShingle A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
Aloise,Daniel
clustering
sum-of-squares
semidefinite programming
title_short A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
title_full A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
title_fullStr A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
title_full_unstemmed A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
title_sort A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering
author Aloise,Daniel
author_facet Aloise,Daniel
Hansen,Pierre
author_role author
author2 Hansen,Pierre
author2_role author
dc.contributor.author.fl_str_mv Aloise,Daniel
Hansen,Pierre
dc.subject.por.fl_str_mv clustering
sum-of-squares
semidefinite programming
topic clustering
sum-of-squares
semidefinite programming
description Minimum sum-of-squares clustering (MSSC) consists in partitioning a given set of n points into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. Recently, Peng & Xia (2005) established the equivalence between 0-1 semidefinite programming (SDP) and MSSC. In this paper, we propose a branch-and-cut algorithm for the underlying 0-1 SDP model. The algorithm obtains exact solutions for fairly large data sets with computing times comparable with those of the best exact method found in the literature.
publishDate 2009
dc.date.none.fl_str_mv 2009-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000300002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000300002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-74382009000300002
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
dc.source.none.fl_str_mv Pesquisa Operacional v.29 n.3 2009
reponame:Pesquisa operacional (Online)
instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron:SOBRAPO
instname_str Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron_str SOBRAPO
institution SOBRAPO
reponame_str Pesquisa operacional (Online)
collection Pesquisa operacional (Online)
repository.name.fl_str_mv Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
repository.mail.fl_str_mv ||sobrapo@sobrapo.org.br
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