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Variable selection for nonlinear support vector machines via elastic net penalty
Journal of the Korean Data & Information Science Society 2023;34:23-35
Published online January 31, 2023;
© 2023 Korean Data and Information Science Society.

Hoseok Hwang1 · Hosik Choi2 · Changyi Park3

13Department of Statistics, University of Seoul
2Department of Urban Big Data Convergence, University of Seoul
Correspondence to: This work was supported by the 2022 Research Fund of the University of Seoul.
1 Graduate student, Department of Statistics, University of Seoul, Seoul 02504, Korea.
2 Associate professor, Department of Urban Big Data Convergence, University of Seoul, Seoul 02504, Korea.
3 Professor, Department of Statistics, University of Seoul, Seoul 02504, Korea. E-mail:
Received October 20, 2022; Revised November 18, 2022; Accepted November 22, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Support vector machines (SVMs) are learning methods seeking the optimal hyperplane with the maximal margin based on training data. SVMs are widely used in classification problems because they can be applied in various problems and deal with high dimensional data effectively. However, in the presense of many noise variables, the prediction accuracy of a SVM can degrade and the interpretation of the final model is difficult. To remedy these disadvantages, a variable selection method based on the LASSO (least absolute shrinkage and selection operator) penalty can be considered. The elastic net penalty has been proposed in regression to overcome the shortcoming of the LASSO that the LASSO tends to select only one variable among the correlated variables when varaibles are strongly correlated. In this article, we consider a variable selection method in nonlinear classifications adopting the COSSO (component selection and smoothing operator), called the COSSO-SVM. The EL-COSSO-SVM adopting the elastic net instead of the LASSO is introduced. Our method is illustrated to improve the performances both in variable selection and prediction of the COSSO-SVM through simulation studies and real data analyses.
Keywords : COSSO, kernel, LASSO.