中文摘要：

光滑函数能将不光滑模型变为光滑模型，改善支持向量机的回归性能和效率，Lee等人用一个光滑函数逼近ε-不敏感损失函数的平方，提出ε-不敏感的光滑支持向量回归机模型（ε-SSVR）．本文为求ε-不敏感支持向量回归机的新光滑函数，运用插值函数和复合函数的方法，首先求正号函数的光滑逼近，然后将其复合成ε-不敏感损失函数平方的光滑函数，得到一类新的光滑函数．并从理论上证明该类光滑函数的逼近精度比以往的光滑函数高一个数量级．实验结果表明回归效果得到改善，从而为支持向量回归机提供一类新的光滑函数．

英文摘要：

Smoothing functions can transform the unsmooth support vector machines （SVMs） into smooth ones, and thus better regression results are generated. A smoothing function was used by Lee et al. to approximate the square of ε-insensitive loss function, therefore the ε-insensitive smooth support vector regression （ε-SSVR） was proposed. In this paper, using techniques of interpolation function and function composition, a kind of smoothing functions is proposed for ε-insensitive support vector regressions （SVRs）. Smooth approximations of the plus function are firstly derived and then applied to approximate the square of the ε-insensitive loss function. Theoretical analysis shows that the approximation accuracy of the proposed smoothing functions is an order of magnitude higher than that of the existing ones. Better regression results are yielded and the new kind of smoothing functions is provided for SVRs.