NONPARALLEL HYPERPLANES PROXIMAL CLASSIFIERS BASED ON MANIFOLD REGULARIZATION FOR LABELED AND UNLABELED EXAMPLES

This paper proposes two Laplacian nonparallel hyperplane proximal classifiers (LapNPPCs) for semi- supervised and full-supervised classification problem respectively by adding manifold regularization terms, which are able to exploit the intrinsic structure of the patterns of the training set.

Abstract

In this paper, we propose two Laplacian nonparallel hyperplane proximal classifiers (LapNPPCs) for semi-supervised and full-supervised classification problem respectively by adding manifold regularization terms. Due to the manifold regularization terms, our LapNPPCs are able to exploit the intrinsic structure of the patterns of the training set. Furthermore, our classifiers only need to solve two systems of linear equations rather than two quadratic programming (QP) problems as needed in Laplacian twin support vector machine (LapTSVM) (Z. Qi, Y. Tian and Y. Shi, Neural Netw.35 (2012) 46–53). Numerical experiments on toy and UCI benchmark datasets show that the accuracy of our LapNPPCs is comparable with other classifiers, such as the standard SVM, TWSVM and LapTSVM, etc. It is also the case that based on our LapNPPCs, some other TWSVM type classifiers with manifold regularization can be constructed by choosing different norms and loss functions to deal with semi-supervised binary and multi-class classification problems.