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›› 2017, Vol. 32 ›› Issue (1): 68-77.

Special Issue: Artificial Intelligence and Pattern Recognition

• Data Management and Data Mining •

### Sparse Support Vector Machine with Lp Penalty for Feature Selection

Lan Yao1, Feng Zeng2,*, Member, CCF, Dong-Hui Li3, and Zhi-Gang Chen2, Senior Member, CCF

1. 1 College of Mathematics and Econometrics, Hunan University, Changsha 410082, China;
2 School of Software, Central South University, Changsha 410083, China;
3 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
• Received:2016-02-28 Revised:2016-09-07 Online:2017-01-05 Published:2017-01-05
• Contact: Feng Zeng E-mail:fengzeng@csu.edu.cn
• About author:Lan Yao is an assistant professor of the College of Mathematics and Econometrics, Hunan University, Changsha. She got her B.S. degree in computer science, M.S. and Ph.D. degrees in applied mathematics from Hunan University, Changsha, in 2000, 2006 and 2014 respectively. Her research interests include data mining, numerical methods in optimization and network optimization.
• Supported by:

This work is supported in part by the National Natural Science Foundation of China under Grant Nos. 61502159, 61379057, 11101081, and 11271069, and the Research Foundation of Central South University of China under Grant No. 2014JSJJ019.

We study the strategies in feature selection with sparse support vector machine (SVM). Recently, the socalled L p-SVM (0< p< 1) has attracted much attention because it can encourage better sparsity than the widely used L1-SVM. However, Lp-SVM is a non-convex and non-Lipschitz optimization problem. Solving this problem numerically is challenging. In this paper, we reformulate the Lp-SVM into an optimization model with linear objective function and smooth constraints (LOSC-SVM) so that it can be solved by numerical methods for smooth constrained optimization. Our numerical experiments on artificial datasets show that LOSC-SVM (0< p< 1) can improve the classification performance in both feature selection and classification by choosing a suitable parameter p. We also apply it to some real-life datasets and experimental results show that it is superior to L1-SVM.

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