A rough margin-based ν-twin support vector machine

Twin support vector machine (TSVM) is a new machine learning algorithm, which aims at finding two nonparallel planes for each class. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one. However, when constructing the classification plane for one class, a large number of samples of this class are considered in the objective function, but only fewer samples in the other class are considered, which easily results in over-fitting problem. In addition, the same penalties are given to each misclassified samples in the TSVM. In fact, the misclassified samples have different effects on the decision of the hyper-plane. In order to overcome these two disadvantages, by introducing the rough set theory into nu-TSVM, we propose a rough margin-based nu-TSVM in this paper. In the proposed algorithm, the different points in the different positions are proposed to have different effects on the separating hyper-plane. We firstly construct rough lower margin, rough upper margin, and rough boundary in the nu-TSVM and then give the different penalties to the different misclassified samples according to their positions. The new classifier can avoid the over-fitting problem to a certain extent. Numerical experiments on one artificial dataset and six benchmark datasets demonstrate the feasibility and validity of the proposed algorithm.