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中文摘要：
光滑函数将不光滑的模型变为光滑模型,改善支持向量回归机的回归性能和效率,从而降低计算的复杂性.寻找性能更好的光滑函数是研究光滑向量回归机的一个关键问题.本文用级数展开的方法得出了ε–不敏感的支持向量回归机｜x｜ε2的一类新的光滑函数.证明了这类函数的性能,它能满足任意阶光滑的要求,也能达到任意给定的逼近精度.实验结果表明,随着光滑阶数的提高,逼近精度和回归性能也相应提高.从而为支持向量回归机和相关研究领域提供了一类新的、性能更好的多项式光滑函数.
英文摘要：
Smoothing functions can transform the unsmooth support vector regressions into smooth ones,and thus better regression results can be obtained.It has been one of the key problems to seek a better smoothing function in this field for a long time.Using the series expansion,a new class of polynomial smoothing functions is proposed for the ｜x｜ε2 function in ε-insensitive support vector regressions.Their important properties are then discussed.It is shown that the approximation accuracy and smoothness rank of polynomial functions can be as high as required.The experimental results show that as the smoothness rank of polynomial functions increases,the approximation accuracy and the regression performance are correspondingly improved.Therefore,the new class of polynomial functions provides better performance for smoothing the support vector regression.
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