基于二次多项式的光滑支持向量机在分类中的若干问题

Several Problems of Smooth Support Vector Classifiers Based on 2nd-order Polynomial

袁玉波等人采用一个二次多项式作为光滑函数,提出一个基于二次多项式的光滑支持向量机。然而,这种光滑支持向量机作为一种新模型,还存在如下4个尚待解决的问题:能否用其它二次多项式作为光滑函数,构建光滑支持向量机?这种光滑支持向量机有多少个?其收敛性如何?其分类效果如何?本文从二次多项式入手,分析了二次多项式作为光滑函数的问题,还分析了基于二次多项式的光滑支持向量机问题,解决了上述四个问题。

Yuan et al use a 2nd-order polynomial as a smoothing function, and propose a smooth support vector machine based on 2nd-order polynomial. As a new smooth model, there are four problems ： Can other 2nd-order polynomials be used as smoothing functions to obtain other smooth support vector machines？ How many are there in tiffs class of smooth model？ Do these smooth models converge？ Is the performance of classification improved？ This paper addresses these problems by studying 2nd-order polynomials as smoothing functions and the resuhant 2nd-order polynomial smooth support vector machines. Finally, it solves the above four problems.