In this work, two novel formulations for embedded feature selection are presented. A second-order cone programming approach for Support Vector Machines is extended by adding a second regularizer to encourage feature elimination. The one- and the zero-norm penalties are used in combination with the Tikhonov regularization under a robust setting designed to correctly classify instances, up to a predefined error rate, even for the worst data distribution. The use of the zero norm leads to a nonconvex formulation, which is solved by using Difference of Convex (DC) functions, extending DC programming to second-order cones. Experiments on high-dimensional microarray datasets were performed, and the best performance was obtained with our approaches compared with well-known feature selection methods for Support Vector Machines.
Bibliographical noteFunding Information:
The first author was supported by FONDECYT project 1160894, the second was funded by FONDECYT project 1160738, and third author was supported by FONDECYT project 1130905. This work was partially funded by Complex Engineering Systems Institute (CONICYT, PIA, FB0816). The authors are grateful to the anonymous referees for their careful reading and helpful suggestions that improved the paper greatly.
© 2017 Elsevier Inc.
- Dc algorithm
- Second-order cone programming
- Support vector machines
- Zero norm