Localized Proximal Support Vector Machine via Generalized Eigenvalues
Xu Yang · Chinese Journal of Computers · 2007
A binary classifier termed as proximal support vector machine via generalized eigenvalues (GEPSVM), is proposed recently. It aims to obtain two nonparallel planes generated from their corresponding generalized eigenvalue problem and has equivalent test correctness to SVM. In nature, GEPSVM attempts fitting two-class points with two planes. For an unseen sample, according to decision rule of GEPSVM, it will be assigned to the closest planes. In fact, this rule, in most cases, may result in poor test correctness. In this paper, based on GEPSVM, a new classifier named Localized GEPSVM is presented. Instead of two fitting planes, an unknown sample will be classified to the closest localized planes, i.e., convex hull, which are generated from the projections of two-class training points, respectively. Compared to GEPSVM, LGEPSVM outperforms GEPSVM in test correctness. Derivatively, LGEPSVM also develops an algorithm for solving convex hull on the projective hyperplane. Besides simple geometrical interpretation, this algorithm eases up to kernel version. Finally, Test accuracy of LGEPSVM algorithms will be validated on some artificial and real UCI datasets.