Efficient approaches for ℓ 2-ℓ 0 regularization and applications to feature selection in SVM

摘要

For solving a class of ℓ 2- ℓ 0- regularized problems we convexify the nonconvex ℓ 2- ℓ 0 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.