一类新型的光滑支持向量分类机

摘要

为了解决支持向量机中非光滑问题，基于贝塞尔函数提出一范式的贝塞尔光滑支持向量机模型，并证明了贝塞尔函数的光滑性和收敛性，分析了其对正号函数的逼进性能。根据模型的特点，应用Armijo⁃Newton方法进行求解，理论分析和数值实验结果都证明贝塞尔光滑支持向量机在分类性能上优于以往提出来的光滑模型。%To Solve the non⁃smooth problems of support vector maehine(SVM). In this paper, a class of 1⁃norm Bezier function support vector machine model ( BSSVM1 ) is proposed based on Bezier function. Moreover, the smoothness of Bezier function is proved and its approach degree is analyzed. According to the property of the model, Newton⁃Armijo algorithm is applied to solving the BSSVM1 model. Our theoretical analysis and numerical experi⁃ments confirm that the BSSVM1 model have a better classification performance than smooth models proposed previ⁃ously.