求解非正定核Huber-SVR的SMO算法

通过运用SMO分解思想和支持向量回归机SVR模型的约束条件,将SVR模型的求解问题转化成一系列的给定区间内抛物线的最小值求解问题,对于非正定核而言由于只改变其中部分抛物线的开口方向,因而可以求得其最小值.据此提出了一种可以求解非正定核的Huber-SVR的SMO方法,推导出了相应的迭代公式并设计了相应的算法.由于用该算法可以求解具有非正定核的SVR,因此可用具有非正定核的Huber-SVR进行回归和预测实验,并与正定核的Huber-SVR的实验结果进行比较.实验表明,对于Huber-SVR而言,某些非正定核比正定核有更好的回归和预测性能,这说明了求解非正定核的Huber-SVR的SMO算法的有效性和必要性.这一算法也可以推广到其它SVR中.

SMO Algorithm for Resolving Huber-SVR with Non-positive Kernels

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.