DCA for Sparse Quadratic Kernel-Free Least Squares Semi-Supervised Support Vector Machine

Abstract

With the development of science and technology, more and more data have been produced. For many of these datasets, only some of the data have labels. In order to make full use of the information in these data, it is necessary to classify them. In this paper, we propose a strong sparse quadratic kernel-free least squares semi-supervised support vector machine (SSQLSS3VM), in which we add a ℓ0norm regularization term to make it sparse. An NP-hard problem arises since the proposed model contains the ℓ0 norm and another nonconvex term. One important method for solving the nonconvex problem is the DC (difference of convex function) programming. Therefore, we first approximate the ℓ0 norm by a polyhedral DC function. Moreover, due to the existence of the nonsmooth terms, we use the sGS-ADMM to solve the subproblem. Finally, empirical numerical experiments show the efficiency of the proposed algorithm.