A second-order cone programming formulation for twin support vector machines

Sebastián Maldonado; Julio López; Miguel Carrasco

doi:10.1007/s10489-016-0764-4

A second-order cone programming formulation for twin support vector machines

Sebastián Maldonado^*, Julio López, Miguel Carrasco

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

Second-order cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classification. These formulations study the worst-case setting for class-conditional densities, leading to potentially more effective classifiers in terms of performance compared to the standard SVM formulation. In this work we propose an SOCP extension for Twin SVM, a recently developed classification approach that constructs two nonparallel classifiers. The linear and kernel-based SOCP formulations for Twin SVM are derived, while the duality analysis provides interesting geometrical properties of the proposed method. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance compared to alternative SVM methods.

Original language	English
Pages (from-to)	265-276
Number of pages	12
Journal	Applied Intelligence
Volume	45
Issue number	2
DOIs	https://doi.org/10.1007/s10489-016-0764-4
State	Published - 1 Sep 2016

Bibliographical note

Funding Information:
The first author was supported by FONDECYT project 1140831, the second was funded by CONICYT Anillo ACT1106, and third author was supported by FONDECYT project 1130905. Support from the Chilean “Instituto Sistemas Complejos de Ingeniería” (ICM: P-05-004-F, CONICYT: FB016, www.sistemasdeingenieria.cl ) is greatly acknowledged.

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Second-order cone programming
Support vector classification
Twin support vector machines

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10.1007/s10489-016-0764-4

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title = "A second-order cone programming formulation for twin support vector machines",

abstract = "Second-order cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classification. These formulations study the worst-case setting for class-conditional densities, leading to potentially more effective classifiers in terms of performance compared to the standard SVM formulation. In this work we propose an SOCP extension for Twin SVM, a recently developed classification approach that constructs two nonparallel classifiers. The linear and kernel-based SOCP formulations for Twin SVM are derived, while the duality analysis provides interesting geometrical properties of the proposed method. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance compared to alternative SVM methods.",

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note = "Funding Information: The first author was supported by FONDECYT project 1140831, the second was funded by CONICYT Anillo ACT1106, and third author was supported by FONDECYT project 1130905. Support from the Chilean “Instituto Sistemas Complejos de Ingenier{\'i}a” (ICM: P-05-004-F, CONICYT: FB016, www.sistemasdeingenieria.cl ) is greatly acknowledged. Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

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doi = "10.1007/s10489-016-0764-4",

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AU - López, Julio

AU - Carrasco, Miguel

N1 - Funding Information: The first author was supported by FONDECYT project 1140831, the second was funded by CONICYT Anillo ACT1106, and third author was supported by FONDECYT project 1130905. Support from the Chilean “Instituto Sistemas Complejos de Ingeniería” (ICM: P-05-004-F, CONICYT: FB016, www.sistemasdeingenieria.cl ) is greatly acknowledged. Publisher Copyright: © 2016, Springer Science+Business Media New York.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - Second-order cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classification. These formulations study the worst-case setting for class-conditional densities, leading to potentially more effective classifiers in terms of performance compared to the standard SVM formulation. In this work we propose an SOCP extension for Twin SVM, a recently developed classification approach that constructs two nonparallel classifiers. The linear and kernel-based SOCP formulations for Twin SVM are derived, while the duality analysis provides interesting geometrical properties of the proposed method. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance compared to alternative SVM methods.

AB - Second-order cone programming (SOCP) formulations have received increasing attention as robust optimization schemes for Support Vector Machine (SVM) classification. These formulations study the worst-case setting for class-conditional densities, leading to potentially more effective classifiers in terms of performance compared to the standard SVM formulation. In this work we propose an SOCP extension for Twin SVM, a recently developed classification approach that constructs two nonparallel classifiers. The linear and kernel-based SOCP formulations for Twin SVM are derived, while the duality analysis provides interesting geometrical properties of the proposed method. Experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance compared to alternative SVM methods.

KW - Second-order cone programming

KW - Support vector classification

KW - Twin support vector machines

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SP - 265

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JO - Applied Intelligence

JF - Applied Intelligence

IS - 2

ER -

A second-order cone programming formulation for twin support vector machines

Abstract

Bibliographical note

Keywords

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