A v-twin support vector machine (v-TSVM) classifier and its geometric algorithms

In this paper, a v-twin support vector machine (v-TSVM) is presented, improving upon the recently proposed twin support vector machine (TSVM). This v-TSVM introduces a pair of parameters (v) to control the bounds of the fractions of the support vectors and the error margins. The theoretical analysis shows that this v-TSVM can be interpreted as a pair of minimum generalized Mahalanobis-norm problems on two reduced convex hulls (RCHs). Based on the well-known Gilbert's algorithm, a geometric algorithm for TSVM (GA-TSVM) and its probabilistic speed-up version, named PGA-TSVM, are presented. Computational results on several synthetic as well as benchmark datasets demonstrate the significant advantages of the proposed algorithms in terms of both computation complexity and classification accuracy. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.