A General Formulation of Polynomial Smooth Support Vector Machines

Yuan et al. used a polynomial function as smoothing function, and proposed a polynomial smooth support vector machine （PSSVM） in 2005, which improved the performance and efficiency of SVM for classification. Using the technique of interpolation functions, Xiong et al. developed a recursive formula to obtain a new class of smoothing functions, and solved the problems of existence and seeking better smoothing functions in 2007. However, problems still exist in looking for other smooth models and the general formulation of the polynomial smooth support vector machines. A class of polynomial functions is applied as new smoothing functions, and a dth-order polynomial smooth support vector machine （dPSSVM） is proposed using the smoothing technique, which is a general formulation of polynomial smooth support vector machines. The global convergence of dPSSVM is proved by a mathematical inductive method, and experiments are carried out to evaluate dPSSVM. The numerical results show that the performance and efficiency of dPSSVM are best, and better than that of the PSSVM when its smooth order is 3, but after its smooth order is greater than 3, the performance of classification is almost the same while the efficiency becomes worse. The problem of general formulation is successfully solved for polynomial smooth support vector machines.