A regularization for the projection twin support vector machine

For the recently proposed projection twin support vector machine (PTSVM) [1], we propose a simpler and reasonable variant from theoretical point of view, called projection twin support vector machine with regularization term, RPTSVM for short. Note that only the empirical risk minimization is introduced in primal problems of PTSVM, incurring the possible singularity problems. Our RPTSVM reformulates the primal problems by adding a maximum margin regularization term, and, therefore, the singularity is avoided and the regularized risk principle is implemented. In addition, the nonlinear classification ignored in PTSVM is also considered in our RPTSVM. Further, a successive overrelaxation technique and a genetic algorithm are introduced to solve our optimization problems and to do the parameter selection, respectively. Computational comparisons of our RPTSVM against original PTSVM, TWSVM and MVSVM indicate that our RPTSVM obtains better generalization than others.