基于特征值分解的最大间隔支持向量回归机

Maximum margin eigenvalue proximal support vector regressor

广义特征值中心支持向量回归机(GEPSVR)是一种有效的核回归算法,但其在求解优化问题时易导致奇异性问题.为此,提出一种基于特征值分解的支持向量回归机,简称IGEPSVR.与GEPSVR相比,IGEPSVR的主要优势有:结合最大间隔准则和GEPSVR几何思想给出了新的距离度量准则;在优化模型中引入Tikhonov正则项,克服了可能产生的奇异性问题;IGEPSVR仅需求解两个标准特征值,降低了计算复杂度.实验结果表明,较GEPSVR算法,IGEPSVR不仅提高了学习能力,而且缩短了训练时间.

The generalized eigenvalue proximal support vector regressor（GEPSVR） is an effective kernel-based regression algorithm. However, the generalized eigenvalue problems may be ill-conditioned in the GEPSVR. Therefore, a maximum margin eigenvalue proximal support vector regressor（IGEPSVR） is proposed. The main advantages are as following by defining the distances between the insensitive functions and data points, a novel optimization model is proposed according to the maximum margin criterion and GEPSVR; the possible ill-conditioned problem is overcome by introducing the meaningful Tikhonov regularization terms; the generalized eigenvalue decomposition is replaced by the standard eigenvalue decomposition, leading to simpler optimization problems. Experimental results on a series of datasets show that IGEPSVR is superior to GEPSVR in both generalization and training speed.