关键词: 支持向量机, 光滑函数, 回归, &epsilon, -不敏感损失函数

Abstract:

Xiong et al. proposed a method in 2008, which can develop infinite smoothing functions for εinsensive support vector regression (εSVRs) in a theoritical sense, but whose reasoning process is very complex. Using the smoothing functions of support vector machine for classification, 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.

Key words: support vector machine;smoothing function；regression;εinsensive loss function