从SVC核到SVR核的非正定问题的研究

ON NON-POSITIVE DEFINITE PROBLEM OF KERNEL FUNCTION FROM SVC TO SVR

从支持向量回归机的几何框架出发,用理论推导和仿真的方法,提出了两种从SVC到SVR的核函数转换中引起的核函数非正定性问题的解决方法。一是通过引入空间映射变换保证所得到的SVR的核函数是正定的;二是利用近似SVR模型解决具有非正定核的SVR模型的不可解问题。仿真结果表明,该两种方法能够基本解决上述问题。

Proceeding from geometric framework of SVR,we find out two ways to solve the non-positive definite problem of kernel function induced from transforming SVC to SVR with both theoretical derivation and emulation methods.The first way is to ensure the kernel function to be positive definite by introducing space mapping transformation;the second way is using similar-SVR model to solve the unsolvable problem of SVR model with non-positive definite kernel function.Emulation experimental results show that these two methods expressed in this article can basically solve above problem.