【摘要】 根据数据特征构造核函数是当前SVM(支持向量机)的难点,文章采用重构数据样本相似度曲面的方法构造三种新的核函数.证明前两种核是Mercer核,并且讨论了三种核的存在性、稳定性和唯一性.指出核函数的本质是表达相似性的工具,核函数与Mercer条件、正定性、对称性互为非充分非必要条件.仿真研究表明,本核函数对学习样本本身的分类是完美的,而且其泛化能力优于传统核函数的SVM.更多还原

【Abstract】 In order to overcome the difficulties in constructing kernel function with data feature for current su-pport vector machines(SVMs),this paper constructs three new kernel functions by reconstructing the similarity surface of data samples.It is proved that the first two are Mercer kernels,and the existence,stability and uniqueness of the three kernels are discussed.Kernel functions are in essence a tool to measure comparability,and there exists a mutually unnecessary and insufficient condition between kernel function,Mercer condition,positive definiteness and symmetry.Simulation shows that the presented kernel function can perfectly classify the learning samples,and its generalization ability is superior to the SVMs based on traditional kernel functions.更多还原