Bounded locality preserving distance based generalized eigenvalue proximal support vector machine

Abstract

Generalized eigenvalue proximal support vector machine (GEPSVM) is regarded as a milestone in the development of the powerful SVMs. It is more suitable to solve the XOR problem than SVM, meanwhile, it is faster. However, GEPSVM and SVM do not consider the local geometrical structure information of training samples. In this paper, we propose a bounded locality preserving distance based generalized eigenvalue proximal support vector machine, called BLPD-GEPSVM in short. It incorporates the locality preserving matrix and the regularization term of structural risk minimization into GEPSVM formulation. The locality preserving matrix reflects the distance of points within class, while the structural risk reflects the distance between two different classes. In this way, the proposed method not only takes into account the local geometrical structure between samples, but also enhances the global discriminant ability of GEPSVM. Experimental results conducted on the artificial datasets and UCI datasets indicate that our BLPD-GEPSVM shows quite competitive performance compared to the GEPSVM, and is more efficient than the benchmark SVM.