基于样条函数的光滑支持向量机模型

Smooth support vector machine model based on spline functions

应用光滑函数改进支持向量机模型,得到无约束条件、可微的二次规划问题,从而可以采用快速的最优化算法求解光滑支持向量机模型.提出了一种广义三弯矩方法,用这个方法构造出新的五次样条光滑函数和七次样条光滑函数.证明了上述两个样条光滑函数的逼近精度均高于已有的各种光滑函数;基于上述两个样条函数的光滑支持向量机模型的收敛精度也高于已有的各种光滑支持向量机模型.

Differentiable and unconstrained quadratic programming can be constructed by improving a support vector machine （SVM） model using a smooth function, and thus a lot of fast optimization algorithms can be applied to solve the smooth SVM model. A new five-order spline function and a new seven-order spline function were constructed by a general three-moment method. These two spline functions are proved that their approximation accuracy is better than any other smooth functions, and the convergence accuracy of the spline function SVM model based on the five-order spline or seven-order spline is higher than any other smooth SVM models.