求解非半正定核Huber-支持向量回归机问题的序列最小最优化算法

Sequential-minimal-optimization algorithm for solving Huber-suppor-vector-regression with non-positive semi-definite kernels

序列最小最优化(SMO)算法是求解大型支持向量机(SVM)问题的有效算法.已有的算法都要求核函数是正定的或半正定的,从而使其应用受到限制.针对这种缺点,本文提出一种新的的SMO算法,可求解非半正定核Huber-SVR问题.提出的算法在保证收敛的前提下可使非半正定Huber-SVR能够达到比较理想的回归精度,因而具有一定的理论意义和实用价值.

Sequential-minimal-optimization（SMO） algorithm is effective in solving large-scale support-vectormachine（SVM） problems. However, the existing algorithms require the kernel functions to be positive definite（PD） or positive semi-definite（PSD）, thus limiting their applications. Having considered their deficiencies, we propose a new al- gorithm for solving Huber-SVR problems with non-positive semi-definite（non-PSD） kernels. This algorithm provides desirable regression-accuracies while ensuring the convergence. Thus, it is of theoretical and practical significance.