Interplation Smooth Technology For Smooth Support Vector Machine

Support Vector Machines evolved from the Statistical Learning Theory is a new method for Data Mining. It's a kind of machine learning algorithms based on Structural Risk Minimization. Comparing to the traditional machine learning algorithms, SVM is a good solution while encountered in non-linear, high dimension, local minimum and so on. SVM has been widely studied and applied recently, Smooth Support Vector Machine, a latest important branch of support vector machines, has better speed in learning comparing with traditional algorithms and deformations of SVM while it achieves better learning generalization ability.In this paper, theoretical foundation of SVM, mainly include the VC-dimensional theory and the principle of structural risk minimization in Statistical Learning Theory, will be introduced at beginning, as well as the model of SSVM. smooth techniques for SSVM, including the integral function of Sigmoid function initially proposed by SSVM, piecewise function based on sub-arc curve function and piecewise polynomial function will be anlysised. The main content of this paper is interpolation polynomial technology base on three interplation points, two situations including general region and symmertric region on both sides of the origin will be discussed. The courses of how to establish the optimization model and how to sovle the optimize problem for gaining the best polynomial functions in symmetric region will be given. Two 2-order smooth functions with three and four times, applying in SSVM, were got by the optimization model. A particular circumstance of indirectly interpolation base on three interpolation points is considered. For each smooth function in this paper, the theoretical basis, the detailed derivation process and performance are described.Base on simulated data, numerical experiment training smooth support vector classifier machine with all different kinds of smooth functions will be given. The better approximation for the plus function for the smooth function, the SSVM has better generalization ability, the more complex calculation for the smooth function, more training time will be consumed. So we should find a smooth function can achieve best generalization ability and least training time by balancing the approximation to the plus function and the calculation for the smooth function while in practical application.