光滑支持向量机多项式函数的研究

Research on polynomial functions for smoothing support vector machines

为了找到多项式光滑支持向量机(polynomial smooth support vector machine,PSSVM)中性能更好的光滑函数,将正号函数变形并展开为多项式级数,得到一类光滑函数。证明了这类函数的性能,它既能满足任意阶光滑的要求,也能达到任意给定的逼近精度。用Newton-Armijo算法求解相应的PSSVM模型,实验结果表明,随着多项式光滑函数阶数的提高,逼近精度和相应PSSVM模型的分类性能也相应提高。

To find smoothing functions with good performance, a plus function is transformed into an equivalent infinite series, thus deriving a class of polynomial smoothing functions. The important properties of them are discussed. It is shown that the approximation accuracy and smoothing rank of polynomial functions can be as high as required. The Newton-Armijo algorithm is used to solve the polynomial smooth support vector machine （PSSVM） finally. The experimental results show that as the smoothing rank of polynomial functions increases, the approximation accuracy and the classification performance of the PSSVM mode are correspondingly improved.