光滑函数在支持向量机中起着重要作用。Chen和Mangasarian提出了Sigmoid函数的积分函数,袁玉波等人提出了一个一阶光滑的多项式函数。然而,一阶光滑的多项式函数是否唯一的问题尚未得到解决。本文用反证法分析了该类多项式函数,经证明,一阶光滑的多项式函数是唯一的,为研究光滑支持向量机提供了更好的理论支持。 Smoothing functions play an important role in SVM. Chen and Mangasarian proposed the integral function of Sigmoid function, Yuan Yubo et al. Proposed a first-order smooth polynomial function. However, the only problem with first-order smooth polynomial functions has not yet been solved. In this paper, we analyze the polynomial function by the way of inverse proof. It is proved that the first-order smooth polynomial function is unique and provides a better theoretical support for the research of smooth support vector machines.