关键词: 非正定核，核方法，SMO算法，支持向量回归机

Abstract: A new SMO algorithm for SVR was proposed which can solve the SVR with non-positive kernels. In our SMO algorithm, the problem of solving SVR model is decomposed into a series of sulrproblems of seeking the minimum of parabola within a limited range. Such minimum can be found because only the symmetry axis direction of some parabo las is changed as respect to non- positive kernels. Hence,we derived relevant iterative formula of SMO method for Huber-SVR and designed the relevant algorithm. Some necessary proofs about the algorithm were also given. Based on our SMO algorithm, we did both regression experiments and prediction experiments using Huber-SVR with non-positive kernels, and compared the experimental results with that of Huber-SVR with positive kernels. The experimental results showed that some non-positive kernels may have better regression performance and better prediction performance than positive kernels,and this confirmed the validity and necessity of our algorithm. This method can also be extended to the other SVR.

Key words: Non-positive kernel, Kernel method, SMO algorithm, SVR