A novel margin-based twin support vector machine with unity norm hyperplanes

For classification problems, twin support vector machine (TWSVM) determines two nonparallel hyperplanes by solving two related SVM-type problems. TWSVM classifies binary patterns by the proximity of it to one of the two nonparallel hyperplanes. Thus, to calculate the distance of a pattern from the hyperplane, we need the unity norm of the normal vector of the hyperplane. But in the formulation of TWSVM, these equality constraints were not considered. In this paper, we consider unity norm constraints by using Euclidean norm and add a regularization term with the idea of maximizing some margin in TWSVM and propose a novel margin-based twin support vector machines with unity norm hyperplanes (UNH-MTSVM). We solved UNH-MTSVM by Newton's method, and the solution is updated by conjugate gradient method. The performance of both the linear and nonlinear UNH-MTSVM is verified experimentally on several bench mark and synthetic datasets. Experimental results show the effectiveness of our methods in both computation time and classification accuracy.