Hoai An Le Thi, Tao Pham Dinh, Mamadou Thiao, Efficient approaches for l2-l0 regularization and applications to feature selection in SVM.

Abstract: For solving a class of l2-l0-regularized problems we convexify the nonconvex  l2-l0 term with the help of its biconjugate function. The resulting convex program is explicitly given which possesses a very simple structure and can be handled by convex optimization tools and standard softwares. Furthermore, to exploit simultaneously the advantage of convex and nonconvex approximation approaches, we propose a two phases algorithm in which the convex relaxation is used for the first phase and in the second phase an efficient DCA (Difference of Convex functions Algorithm) based algorithm is performed from the solution given by Phase 1. Applications in the context of feature selection in support vector machine learning are presented with experiments on several synthetic and real-world datasets. Comparative numerical results with standard algorithms show the efficiency the potential of the proposed approaches.

 

Keywords: sparsity, zero norm, convex relaxation, biconjugate function, nonconvex approximation, DC programming, DCA, feature selection in SVM.

 

Citation: Hoai An Le Thi, Tao Pham Dinh, Mamadou Thiao, Efficient approaches for l2-l0 regularization and applications to feature selection in SVM. To appear in Applied Intelligence (2016).