基于插值的核函数构造

近年来，统计学习(SLT)和支持向量机(SVM)理论的研究日益受到当前国际机器学习领域的重视．有关核函数的研究则一直是研究的重点．这是因为不同的核函数会导致SVM的泛化能力有很大的不同．如何根据所给数据选择合适的核函数成为人们所关注的核心问题．该文首先指出满足Mercer条件的核函数的具体表达式并非问题关键，在此基础上，该文进一步提出利用散乱数据插值的办法确定特征空间中感兴趣点的内积值以代替传统核函数的一般表达式所起的作用．实验表明该方法不仅能够有效改善支持向量机的设计训练过程中的不确定性，而且泛化能力要优于绝大部分的基于传统核函数的支持向量机．

Interpolation Based Kernel Function's Construction

The kernel function is important for support vector machines(SVMs) in classifying and regression. However, how to select a kernel function for the given data is still an open problem. Many papers are limited to consult the properties of some standard kernel functions. Since the effect of kernel mapping has not been understood very clearly, the result may be not as good as SVM should be in some cases. In this paper, we first point out that it is no necessary to get the explicit expression of mercer kernel functions, because only some limited values are needed in SVM. Then we present a method based on scattered data interpolation to construct a kernel function according to the given data. The experiments show that kernel function constructed in our method has less subjectivity and more predominance of generalization than most of traditional kernel functions.