lp-norm support vector machine with CCCP

This paper proposed an efficient model l_p-support vector classification(l_p-SVC) which combines C-SVC and feature selection strategy by introducing the l_p-norm (0 <; p <; 1). Following a lower bound for the absolute value of nonzero entries in every local optimal solution of the model, we investigated the relationship between sparsity of the solution and the choice of the regularization parameter and p-norm. In order to solve the nonconvex problem in l_p-SVC, we investigate an iteratively reweighted l_q(q ≥ 1) convex relaxation scheme, in which the weighted problem solved by CCCP, and preliminary numerical experiments show the superior effectiveness of our model for identifying nonzero entries in numerical solutions and feature selection than standard l₁ convex relaxation. We also apply it to a real-life credit dataset to prove its efficiency.