Smooth Twin Support Vector Machines via Unconstrained Convex Minimization

Abstract

In this paper, we proposed two smoothing approaches for an implicit Lagrangian twin support vector machine (TWSVM) classifiers by formulating a pair of unconstrained minimization problems in dual variables whose solutions will be obtained using finite Newton method. The idea of our formulation is to reformulate TWSVM as a strongly convex problem by incorporated regularization techniques to improve the robustness. The solution of two modified unconstrained minimization problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems in TWSVM and TBSVM, which leads to extremely simple and fast algorithm. Unlike the classical TWSVM, the structural risk minimization principle is implemented by adding regularization term in the primal problems of our proposed algorithm. This embodies the marrow of statistical learning theory. To demonstrate the effectiveness of the proposed method, we performed numerical experiments on number of interesting real-world datasets and compared their results with other SVMs. Comparison of results with GEPSVM and TWSVM clearly demonstrate the effectiveness and suitability of the proposed method.