Efficient three-way SVM for three-class classification problems

Vivek Srivastava

doi:10.1007/s41060-024-00511-2

Efficient three-way SVM for three-class classification problems

2024-02-18

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DOI：10.1007/s41060-024-00511-2

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Many classification problems in the real world are inherently multi-class. However, most of the classifiers are binary. Solving K-class classification problems with 1-versus-1 approach requires KC2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>KC_2$$\end{document} binary classifiers. Furthermore, it suffers from information loss as other classes are not considered. But, if the solutions of 1-versus-rest approach-based binary classifiers are combined, then the number of classifiers drops to K. Still, it comes with the cost of making the binary class problems imbalanced and nonlinear. K-SVCR is a technique that solves class imbalance problems by giving the 1-versus-1-versus-rest approach, a ternary classifier. But instead of giving any respite on the number of classifiers, researchers again suggest KC2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>KC_2$$\end{document} classifiers. This article attempts to reduce the number of classifiers for three class problems, K=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K=3$$\end{document}. First, it identifies the reason behind the use of so many classifiers with the help of artificially generated datasets. Then, it proposes two methods to identify the correct labelling of classes that bring the best performance of the classifier as a second step. Finally, it verifies if the proposals are effective on the artificial and real-world datasets. Experimental results show that class labelling with proposed methods improved the average accuracy of K-SVCR by 75.3%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$75.3\%$$\end{document} on artificial datasets and 9.97%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$9.97\%$$\end{document} on real-world datasets. In addition to that, the requirement of time and computational resources is reduced to one-third of the original implementation of K-SVCR.

Keywords:

Three-class classification

Support vector machines

Robustness

K-SVCR

Efficient three-way SVM for three-class classification problems

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