PAPER Mixed-Integer Linear Optimization Formulations for Feature Subset Selection in Kernel SVM Classification

We study the mixed-integer optimization (MIO) approach to feature subset selection in nonlinear kernel support vector machines (SVMs) for binary classification. To measure the performance of subset selection, we use the distance between two classes (DBTC) in a high- dimensional feature space based on the Gaussian kernel function. However, DBTC to be maximized as an objective function is nonlinear, nonconvex and nonconcave. Despite the difficulty of linearizing such a nonlinear function in general, our major contribution is to propose a mixed-integer linear optimization (MILO) formulation to maximize DBTC for feature subset selection, and this MILO problem can be solved to optimality using optimization software. We also derive a reduced version of the MILO problem to accelerate our MILO computations. Experimental results show good computational efficiency for our MILO formulation with the reduced problem. Moreover, our method can often outperform the linear-SVMbased MILO formulation and recursive feature elimination in prediction performance, especially when there are relatively few data instances.