基于变异函数的径向基核函数参数估计

THE PARAMETER ESTIMATION OF RBF KERNEL FUNCTION BASED ON VARIOGRAM

研究了支持向量机 (support vector machine,SVM)方法在一定假设条件下 ,核函数取为样本协方差函数时解的具体形式 ,得出了在该假设情况下 SVM方法等价于克立格方法的结论 ,提出了用协方差函数作为 SVM核函数的思想 .考虑到在某些情况下协方差函数可能不存在 ,因此考虑用变异函数来代替协方差函数估计径向基核函数的宽度参数 .这样不仅解决了SVM中径向基核函数宽度参数的确定问题 ,而且把这种情况下的 SVM拟合与概率统计学中的克立格方法联系了起来 ,赋予了

The paper studies the form of the result of SVM with covariance function as the kernel function under some conditions, and draws the conclusion that Kriging is equivalent to SVM under those conditions. Based on the conclusion, we put forward the idea of using the covariance function as a substitute for the RBF kernel function of SVM. Considering that the covariance function could not exist in some conditions, we put forward the idea of using the variogram function as a substitute for the covariance function and prove their equivalence. It not only solves the problem of parameter estimation of SVM kernel function, but also connects the SVM with the Kriging, which gives new statistical meaning to SVM.