光滑函数在支持向量机中起着重要作用,本文研究如何得到一类新的光滑函数.用插值函数的方法导出了一个重要的递推公式,得到了一类新的光滑函数,从而解决了长期困扰人们的一个问题,即如何寻求性能更好的光滑函数问题.还证明了该类函数的若干性能,其逼近精度比 Sigmoid 函数的积分函数高一个数量级,也明显高于一阶和二阶光滑多项式,为支持向量机提供了一类新的光滑函数.

Smoothing functions play an important role in Support Vector Machine(SVM).This paper derived an important recursive formula and a new class of smoothing functions using the technique of interpolation functions.Thus the problem of seeking better smoothing functions was solved,which has been a major obstacle in this field for a long time.Several of its important properties were discussed.It was shown that the approximation accuracy of interpolation functions is better than the integral of the sigmoid function by an order of magnitude.It is also obviously higher than those of the first /second-order smooth polynomial functions.Therefore,the proposed class of interpolation functions is a competitive candidate for smoothing SVM.