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研究半监督支持向量机分类优化模型的非光滑问题.建立了光滑半监督支持向量机模型,采用广义三弯矩法导出零点二阶光滑的广义三次样条函数,并以此逼近半监督支持向量机优化中的非光滑部分.构造出基于上述样条函数的具有一阶光滑的半监督支持向量机,从而可以用优化中的光滑算法来求解该模型.分析了广义三次样条函数逼近对称铰链损失函数的逼近精度,证明了新模型的收敛性.数值实验显示新模型有较好的分类效果.
The problem of nonsmooth problem of semi-supervised SVM classification optimization model is studied.The model of smooth semi-supervised SVM is established and the generalized three-moment method is used to derive the generalized cubic spline function of zero-order second-order smoothness and to approximate the semi-supervised support A smoothing semi-supervised SVM based on the above spline function is constructed, so that the smoothing algorithm in the optimization can be used to solve the model.The generalized cubic spline function approximation symmetry The approximation accuracy of the hinge loss function proves the convergence of the new model. Numerical experiments show that the new model has better classification results.