基于特征值分解的最大间隔支持向量回归机

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.

Maximum margin eigenvalue proximal support vector regressor

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.