Sparse Support Vector Machine with Lp Penalty for Feature Selection

We study the strategies in feature selection with sparse support vector machine （SVM）. Recently, the socalled Lp-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.