Learning Sparse SVM for Feature Selection on Very High Dimensional Datasets

A sparse representation of Support Vector Machines (SVMs) with respect to input features is desirable for many applications. In this paper, by introducing a 0-1 control variable to each input feature, l0-norm Sparse SVM (SSVM) is converted to a mixed integer programming (MIP) problem. Rather than directly solving this MIP, we propose an efficient cutting plane algorithm combining with multiple kernel learning to solve its convex relaxation. A global convergence proof for our method is also presented. Comprehensive experimental results on one synthetic and 10 real world datasets show that our proposed method can obtain better or competitive performance compared with existing SVM-based feature selection methods in term of sparsity and generalization performance. Moreover, our proposed method can effectively handle large-scale and extremely high dimensional problems.