A randomized algorithm for the exact solution of transductive support vector machines

Random sampling is an efficient method for dealing with constrained optimization problems. In computational geometry, this method has been successfully applied, through Clarkson’s algorithm (Clarkson 1996), to solve a general class of problems called violator spaces. In machine learning, Transductiv...

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Authors: Esposito, Gennaro|||0000-0002-9700-2971, Martín Muñoz, Mario|||0000-0002-4125-6630
Format: article
Publication Date:2015
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/83017
Online Access:https://hdl.handle.net/2117/83017
https://dx.doi.org/10.1080/08839514.2015.1035951
Access Level:Open access
Keyword:Supervised learning (Machine learning)
Semisupervised Learning
Transduction Support Vector Machine
Classification
Aprenentatge automàtic
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
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oai_identifier_str oai:upcommons.upc.edu:2117/83017
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repository_id_str
spelling A randomized algorithm for the exact solution of transductive support vector machinesEsposito, Gennaro|||0000-0002-9700-2971Martín Muñoz, Mario|||0000-0002-4125-6630Supervised learning (Machine learning)Semisupervised LearningTransduction Support Vector MachineClassificationAprenentatge automàticÀrees temàtiques de la UPC::Informàtica::Intel·ligència artificialRandom sampling is an efficient method for dealing with constrained optimization problems. In computational geometry, this method has been successfully applied, through Clarkson’s algorithm (Clarkson 1996), to solve a general class of problems called violator spaces. In machine learning, Transductive Support Vector Machines (TSVM) is a learning method used when only a small fraction of labeled data is available, which implies solving a nonconvex optimization problem. Several approximation methods have been proposed to solve it, but they usually find suboptimal solutions. However, a global optimal solution may be obtained by using exact techniques, but at the cost of suffering an exponential time complexity with respect to the number of instances. In this article, an interpretation of TSVM in terms of violator space is given. A randomized method is presented that extends the use of exact methods, thus reducing the time complexity exponentially w.r.t. the number of support vectors of the optimal solution instead of exponentially w.r.t. the number of instances.Peer Reviewed20152015-05-1320162016-02-16journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/83017https://dx.doi.org/10.1080/08839514.2015.1035951reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/830172026-05-27T15:37:01Z
dc.title.none.fl_str_mv A randomized algorithm for the exact solution of transductive support vector machines
title A randomized algorithm for the exact solution of transductive support vector machines
spellingShingle A randomized algorithm for the exact solution of transductive support vector machines
Esposito, Gennaro|||0000-0002-9700-2971
Supervised learning (Machine learning)
Semisupervised Learning
Transduction Support Vector Machine
Classification
Aprenentatge automàtic
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
title_short A randomized algorithm for the exact solution of transductive support vector machines
title_full A randomized algorithm for the exact solution of transductive support vector machines
title_fullStr A randomized algorithm for the exact solution of transductive support vector machines
title_full_unstemmed A randomized algorithm for the exact solution of transductive support vector machines
title_sort A randomized algorithm for the exact solution of transductive support vector machines
dc.creator.none.fl_str_mv Esposito, Gennaro|||0000-0002-9700-2971
Martín Muñoz, Mario|||0000-0002-4125-6630
author Esposito, Gennaro|||0000-0002-9700-2971
author_facet Esposito, Gennaro|||0000-0002-9700-2971
Martín Muñoz, Mario|||0000-0002-4125-6630
author_role author
author2 Martín Muñoz, Mario|||0000-0002-4125-6630
author2_role author
dc.subject.none.fl_str_mv Supervised learning (Machine learning)
Semisupervised Learning
Transduction Support Vector Machine
Classification
Aprenentatge automàtic
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
topic Supervised learning (Machine learning)
Semisupervised Learning
Transduction Support Vector Machine
Classification
Aprenentatge automàtic
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
description Random sampling is an efficient method for dealing with constrained optimization problems. In computational geometry, this method has been successfully applied, through Clarkson’s algorithm (Clarkson 1996), to solve a general class of problems called violator spaces. In machine learning, Transductive Support Vector Machines (TSVM) is a learning method used when only a small fraction of labeled data is available, which implies solving a nonconvex optimization problem. Several approximation methods have been proposed to solve it, but they usually find suboptimal solutions. However, a global optimal solution may be obtained by using exact techniques, but at the cost of suffering an exponential time complexity with respect to the number of instances. In this article, an interpretation of TSVM in terms of violator space is given. A randomized method is presented that extends the use of exact methods, thus reducing the time complexity exponentially w.r.t. the number of support vectors of the optimal solution instead of exponentially w.r.t. the number of instances.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-05-13
2016
2016-02-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/83017
https://dx.doi.org/10.1080/08839514.2015.1035951
url https://hdl.handle.net/2117/83017
https://dx.doi.org/10.1080/08839514.2015.1035951
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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