A lagrangian-based approach for universum twin bounded support vector machine with its applications

The Universum provides prior knowledge about data in the mathematical problem to improve the generalization performance of the classifiers. Several works have shown that the Universum twin support vector machine (U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathfrak {U} $\end{document}-TSVM) is an efficient method for binary classification problems. In this paper, we improve the U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathfrak {U} $\end{document}-TSVM method and propose an improved Universum twin bounded support vector machine (named as IUTBSVM). Indeed, by introducing different Lagrangian functions for the primal problems, we obtain new dual formulations of U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathfrak {U} $\end{document}-TSVM so that we do not need to compute inverse matrices. To reduce the computational time of the proposed method, we suggest a smaller size of the rectangular kernel matrices than the other methods. Numerical experiments on gender classification of human faces, handwritten digits recognition, and several UCI benchmark data sets indicate that the IUTBSVM is more efficient than the other four algorithms, namely U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {U}$\end{document}-SVM, TSVM, U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {U}$\end{document}-TSVM, and IUTSVM in the sense of the classification accuracy.