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A Learning Framework of Nonparallel Hyperplanes Classifier

A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem...

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Detalles Bibliográficos
Autores principales: Yang, Zhi-Xia, Shao, Yuan-Hai, Jiang, Yao-Lin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4488010/
https://www.ncbi.nlm.nih.gov/pubmed/26167527
http://dx.doi.org/10.1155/2015/497617
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author Yang, Zhi-Xia
Shao, Yuan-Hai
Jiang, Yao-Lin
author_facet Yang, Zhi-Xia
Shao, Yuan-Hai
Jiang, Yao-Lin
author_sort Yang, Zhi-Xia
collection PubMed
description A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem when different parameters or loss functions are chosen. Concretely, we discuss the linear and nonlinear cases of the framework, in which we select the hinge loss function as example. Moreover, we also give the primal problems of several extension versions of TWSVM's deformation versions. It is worth mentioning that, in the decision function, the Euclidean distance is replaced by the absolute value |w (T) x + b|, which keeps the consistency between the decision function and the optimization problem and reduces the computational cost particularly when the kernel function is introduced. The numerical experiments on several artificial and benchmark datasets indicate that our framework is not only fast but also shows good generalization.
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spelling pubmed-44880102015-07-12 A Learning Framework of Nonparallel Hyperplanes Classifier Yang, Zhi-Xia Shao, Yuan-Hai Jiang, Yao-Lin ScientificWorldJournal Research Article A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem when different parameters or loss functions are chosen. Concretely, we discuss the linear and nonlinear cases of the framework, in which we select the hinge loss function as example. Moreover, we also give the primal problems of several extension versions of TWSVM's deformation versions. It is worth mentioning that, in the decision function, the Euclidean distance is replaced by the absolute value |w (T) x + b|, which keeps the consistency between the decision function and the optimization problem and reduces the computational cost particularly when the kernel function is introduced. The numerical experiments on several artificial and benchmark datasets indicate that our framework is not only fast but also shows good generalization. Hindawi Publishing Corporation 2015 2015-06-16 /pmc/articles/PMC4488010/ /pubmed/26167527 http://dx.doi.org/10.1155/2015/497617 Text en Copyright © 2015 Zhi-Xia Yang et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Yang, Zhi-Xia
Shao, Yuan-Hai
Jiang, Yao-Lin
A Learning Framework of Nonparallel Hyperplanes Classifier
title A Learning Framework of Nonparallel Hyperplanes Classifier
title_full A Learning Framework of Nonparallel Hyperplanes Classifier
title_fullStr A Learning Framework of Nonparallel Hyperplanes Classifier
title_full_unstemmed A Learning Framework of Nonparallel Hyperplanes Classifier
title_short A Learning Framework of Nonparallel Hyperplanes Classifier
title_sort learning framework of nonparallel hyperplanes classifier
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4488010/
https://www.ncbi.nlm.nih.gov/pubmed/26167527
http://dx.doi.org/10.1155/2015/497617
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