一种求ε-不敏感支持向量回归机光滑函数的新方法

A New Method for Solving the Smooth Functions of ε-Insensive Support Vector Regression

2008年熊金志等人提出了一种求光滑函数的方法,就理论而言可求得ε-不敏感支持向量回归机的无穷个光滑函数,但该方法每次都需要对光滑函数的导数进行积分,推导过程很繁琐。为克服这个缺点,本文利用支持向量分类机的光滑函数,通过相关的理论推导,用新的递推方式来表示支持向量回归机的光滑函数,简化了原方法的推导过程,得到了一种求支持向量回归机光滑函数的新方法。通过用原方法和新方法分别求光滑函数的两个算例,表明了新方法的有效性。还用新方法导出了光滑函数的一个重要性质,即光滑函数关于光滑阶数是单调减函数,为进一步研究光滑支持向量回归机提供了理论依据。

Xiong et al. proposed a method in 2008, port vector regression （ε-SVRs） in a theoritical sense, functions of support vector machine for classification, which can develop infinite smoothing functions for ε-insensive supbut whose reasoning process is very complex. Using the smoothing a new method is proposed by a new recursive way in this paper, whose reasoning process is more simpler. Besides, two examples are put forward to verify the new method. Moverover, an important property of the smoothing functions is deduced with the new method, i. e. , the smoothing functions are monotonicaly decreasing with the smoothing order. This paper supports the theoretical basis for the further research of the smoothing functions of ε-SVRs.