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

In this paper, a ν-twin support vector machine (ν-TSVM) is presented, improving upon the recently proposed twin support vector machine (TSVM). This ν-TSVM introduces a pair of parameters (ν) to control the bounds of the fractions of the support vectors and the error margins. The theoretical analysis shows that this ν-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.