Generalized Twin Support Vector Machines

In this paper, we propose two efficient approaches of twin support vector machines (TWSVM). The first approach is to reformulate the TWSVM formulation by introducing L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document} and L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\infty $$\end{document} norms in the objective functions, and convert into linear programming problems termed as LTWSVM for binary classification. The second approach is to solve the primal TWSVM, and convert into completely unconstrained minimization problem. Since the objective function is convex, piecewise quadratic but not twice differentiable, we present an efficient algorithm using the generalized Newton’s method termed as GTWSVM. Computational comparisons of the proposed LTWSVM and GTWSVM on synthetic and several real-world benchmark datasets exhibits significantly better performance with remarkably less computational time in comparison to relevant baseline methods.