多项式光滑的支持向量回归机一般模型的收敛性研究  

Convergenceness of a General Formulation for Polynomial Smooth Support Vector Regressions

作　　者：熊金志[1] 徐建敏[1] 袁华强[1] 

机构地区：[1]东莞理工学院计算机学院,广东东莞523808

出　　处：《计算机研究与发展》2011年第3期464-470,共7页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(60773050);广东省自然科学基金项目(9151170003000017);广东省科技计划基金项目(2008B060600077;2009B010800054)

摘　　要：2005年Lee等人提出光滑的支持向量回归机模型ε-SSVR(smooth ε-support vector regression),2008年熊金志等人提出一个多项式光滑的支持向量回归机模型ε-PSSVR(polynomialsmoothε-support vector regression),使回归性能及效率得到了一定改善.然而,这种支持向量回归机是否存在一个一般模型,以及一般模型的收敛性等问题没有解决.为此,将一类多项式函数作为新的光滑函数,使用光滑技术,把多项式光滑模型ε-PSSVR推广到一般情形,提出一个多项式光滑的支持向量回归机一般模型ε-dPSSVR(dth-order polynomial smooth ε-support vector regression).并用数学归纳法证明该一般模型的全局收敛性.研究表明:1)多项式光滑的支持向量回归机存在无穷多个模型,可以用一个一般模型来表示;2)该一般模型是全局收敛的,其收敛上界比ε-SSVR缩小半个数量级.成功解决了多项式光滑的支持向量回归机的一般形式及其收敛性问题,为进一步研究多项式光滑的支持向量回归机提供了基本的理论支持.Lee et al.proposed a smooth ε-support vector regression（ε-SSVR）in 2005,and Xiong et al.proposed a polynomial smooth ε-support vector regression（ε-PSSVR）in 2008,which improved the performance and efficiency of regression.However,problems still exist in looking for a general formulation of the polynomial smooth ε-support vector regressions and proving its convergenceness.Therefore,using a class of polynomial functions as new smoothing functions,the polynomial smooth model ε-PSSVR is extended to a general case;and a dth-order polynomial smooth ε-support vector regression（ε-dPSSVR）,which is a general formulation of polynomial smooth ε-support vector regressions,is proposed using the smoothing technique in this paper.The global convergence of ε-dPSSVR is proved by mathematical inductive method.The research concludes that：1）there are an infinite number of polynomial smooth models for support vector regression,which can be described in a general formulation;2）the general formulation is global convergent,and the upper bound of the convergence is reduced about half an order of magnitude to ε-SSVR.The convergence problem of general formulation is successfully solved,which supplies a basic theoretical support for researching polynomial smooth ε-support vector regressions.

关 键 词：回归 支持向量机 光滑 一般模型 收敛 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]