一类三阶多项式光滑的支持向量机

摘要

Using a class of new smoothing functions,the problem of smoothing support vector machines was studied.A new 3rd-order polynomial smooth support vector machine (3SSVM) model was proposed,and its 3rd-order smoothness and global convergence was proved.Numerical experiments were carried out to evaluate the 3SSVM by using Newton-Armijo algorithm.The results show that the 3SSVM model is better than the PSSVM model and the SSVM model,providing better theoretical support for applications of smooth support vector machines.%研究了用一类新的光滑函数对支持向量机作光滑处理的问题,提出了一种新的具有三阶多项式光滑的支持向量机模型3SSVM,证明了该模型具有三阶光滑性和全局收敛性,并用Newton-Armijo算法进行了数值实验.结果表明,3SSVM模型的分类性能和计算速度优于PSSVM模型和SSVM模型,为光滑支持向量机的应用提供了更好的理论支持.