一个广义三次样条光滑半监督支持向量机

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。

A general cubic spline smooth semi-supervised support vector machine

This article is focused on the non-smooth problem of the semi-supervised support vector machine optimization model. A smooth semi-supervised support vector machine model was established. A general cubic spline function with 2 times differentiable at zero point was deduced by a general three-moment method and was used to approach the non-smooth part in the semi-supervised sup-port vector machine. A new smooth semi-supervised support vector with 1 time differentiable based on the general cubic spline function was constructed, and thus a lot of fast optimization algorithms could be applied to solve the smooth semi-supervised vector machine model. The approximation accuracy of the general cubic spline function to the symmetric hinge loss function was analyzed, and the convergence accuracy of the new model was proved. Numerical experiments show that the new model has a better classification result.