Improved Proximal Support Vector Machine via Generalized Eigenvalues

Abstract

GEPSVM [1, 2, 3] does not need to solve quadratic programming problem as for SVM. It can also obtain comparable test set correctness compared to that of SVM. Despite of its successes, GEPSVM may get poor performance when the generalized eigen-equation problem is ill-conditioned. Moreover, it is sensitive to data noise. Aiming at the orientation problems, in this paper, we propose two algorithms: IGEPSVM and IDGEPSVM. Computational results on public datasets from UCI [4] indicate that the proposed IGPSVM can overcome the singular problem appearing in GEPSVM; IDGEPSVM, when influenced by data noise, can obtain better test set correctness than that of GEPSVM, and with comparable training time. All two algorithms obtain two nonparallel planes only through solving the simple eigenvalues problems instead of the generalized eigenvalues problems.