ν-projection twin support vector machine for pattern classification

In this paper, we improve the projection twin support vector machine (PTSVM) to a novel nonparallel classifier, termed as nu-PTSVM. Specifically, our nu-PTSVM aims to seek an optimal projection for each class such that, in each projection direction, instances of their own class are clustered around their class center while keep instances of the other class at least one distance away from such center. Different from PTSVM, our nu-PTSVM enjoys the following characteristics: (i) nu-PTSVM is equipped by a more theoretically sound parameter nu, which can be used to control the bounds of fraction of both support vectors and margin-error instances. (ii) By reformulating the least-square loss of within-class instances in primal problems of nu-PTSVM, its dual problems no longer involve the time-costly matrix inversion. (iii) nu-PTSVM behaves consistent between its linear and nonlinear cases. Namely, the kernel trick can be applied directly to nu-PTSVM for its nonlinear extension. Experimental evaluations on both synthetic and real-world datasets demonstrate the feasibility and effectiveness of the proposed approach. (C) 2019 Elsevier B.V. All rights reserved.