ISSN 1000-1239 CN 11-1777/TP

• 人工智能 •

### 支持向量机多项式光滑函数的误差理论研究

1. (东莞理工学院计算机学院 广东东莞 523808) (hewb@dgut.edu.cn)
• 出版日期: 2016-07-01
• 基金资助:
国家自然科学基金项目(60773050)；广东省科技发展专项资金(基础与应用基础研究方向)项目(2016A030313135)；东莞市科技计划资助项目(201208102027)

### The Error Theory of Polynomial Smoothing Functions for Support Vector Machines

He Wenbin, Liu Qunfeng, Xiong Jinzhi

1. (College of Computer, Dongguan University of Technology, Dongguan, Guangdong 523808)
• Online: 2016-07-01

Abstract: Smoothing functions play an important role in the theory of smooth support vector machines. In 1996, Chen et al proposed a smoothing function of support vector machines—the integral function of Sigmoid function, and solved the error problem of the smoothing function. From 2005 to 2009, Yuan, Xiong and Liu proposed an infinite number of polynomial smoothing function and the corresponding reformulations for support vector machines. However, they did not touch the error functions for this class of polynomial smoothing functions. To fill up this gap, this paper studies the problem of the error functions with the Newton-Hermite interpolation method. The results show that: 1) the error functions of this class of polynomial smoothing functions can be calculated using the Newton-Hermite interpolation method, and the detailed algorithm is given; 2) there are an infinite number of error functions for this class of polynomial smoothing functions and a general formulation is obtained to describe these error functions; 3) there are several important properties for this class of error functions and the strict proof is given for these properties. By solving the problem of the error functions and their properties, this paper establishes an error theory of this class of polynomial smoothing functions, which is a basic theoretical support for smooth support vector machines.