We consider support vector machines for binary classification. As opposed to most approaches we use the number of support vectors (the "L0 norm") as a regularizing term instead of the L1 or L2 norms. In order to solve the optimization problem we use the cross entropy method to search over the possible sets of support vectors. The algorithm consists of solving a sequence of efficient linear programs. We report experiments where our method produces generalization errors that are similar to support vector machines, while using a considerably smaller number of support vectors.

A novel linear feature selection algorithm is presented based on the global minimization of a data-dependent generalization error bound. Feature selection and scaling algorithms often lead to non-convex opti- mization problems, which in many previous approaches were addressed through gradient descent procedures that can only guarantee convergence to a local minimum. We propose an alternative approach, whereby the global solution of the non-convex optimization problem is derived via an equivalent optimization problem. Moreover, the convex optimization task is reduced to a conic quadratic programming problem for which effi- cient solvers are available. Highly competitive numerical results on both artificial and real-world data sets are reported.