中文摘要：

为寻找新的光滑函数，研究光滑函数对光滑支持向量机分类性能的影响，提出分段熵光滑支持向量机模型。给出一个双分支的分段熵函数作为光滑函数，逼近正号函数，分析论证其逼近性能和精度；通过新的光滑函数改进光滑支持向量机模型（SSVM），得到一个新的分段熵光滑支持向量机；验证该光滑支持向量机的正确性和可行性，给出最优解的逼近上限。数值实验结果表明，该分段熵光滑支持向量机分类性能优于SSVM模型。

英文摘要：

To find a new smooth function and study its impact on smooth support vector machine, piecewise entropy smooth sup- port vector machine was proposed. A branch piecewise entropy function was given as smooth function to approximate the plus function. Performances of approaching and approximate error were given for the new smooth function. A new piecewise entropy smooth support vector machine was obtained by improving the model of smooth support vector machine using the new smooth function. The feasibility of this model was verified and its performances were analyzed. The approximation limit of optimum for the new model was given as well. Results of numerical experiments show the new smooth support vector machine has obvious ad- vantages in classification performances over SSVM.