Locality preserving projection twin support vector machine and its application in classification

Abstract

Twin support vector machine (TWSVM) and projection twin support vector machine (PTSVM), are two extensions of traditional support vector machine (SVM). However, TWSVM and PTSVM did not consider the local geometrical structure information of training samples. Therefore, a locality preserving projection twin support vector machine (LPPTSVM) is presented by introducing the basic idea of the locality preserving projection (LPP) into PTSVM. This method not only inherits the ability of TWSVM and PTSVM for dealing with the XOR problem, but also fully considers the local geometrical structure between samples and shows the local underlying discriminatory information. For linear LPPTSVM method, regularization technique is used to overcome the singularity problem, and then the nonlinear LPPTSVM method is constructed by the empirical kernel mapping. Experimental results conducted on the artificial datasets and UCI datasets illustrate the effectiveness of the LPPTSVM method.