【摘要】 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。更多还原

【Abstract】 Smoothing functions play an important role in Support Vector Machines (SVMs). Chen and Mangasarian developed the integration of Sigmoid function, Yuan et al. developed a 1st-order smooth polynomial function. However, the uniqueness problem of 1st-order smooth polynomial function is not resolved yet. With reduction methods, this paper offers a detailed analysis of properties for the polynomial function. The results show that 1st-order smooth polynomial function is unique. The paper provides the better theoretical support for researching the SVM.更多还原