An Interior Point Method for L1/2-SVM and Application to Feature Selection in Classification

Abstract

This paper studies feature selection for support vector machine (SVM). By the use of the $L_{1/2}$ regularization technique, we propose a new model $L_{1/2}$-SVM. To solve this nonconvex and non-Lipschitz optimization problem, we first transform it into an equivalent quadratic constrained optimization model with linear objective function and then develop an interior point algorithm. We establish the convergence of the proposed algorithm. Our experiments with artificial data and real data demonstrate that the $L_{1/2}$-SVM model works well and the proposed algorithm is more effective than some popular methods in selecting relevant features and improving classification performance.