A Fourth-Order Fuzzy Support Vector Machine Based on Class Center

Abstract

In order to deal with the dependence of support vector machine (SVM) on kernel function and the limitation that the decision boundary formed by SVM is a hyperplane when dealing with nonlinear classification tasks, this paper combines the double-well potential function and the idea of fuzzy system and designs a novel SVM variant and a fourth-order fuzzy support vector machine based on class center (FOF-SVM). The FOF-SVM model eschews the use of traditional kernel functions and directly uses quartic hypersurfaces for data modeling. It achieves effective classification of nonlinear data without kernel tricks and reduces the adverse effects of outliers on the overall classification performance. In addition, the specific expression of the model is derived by solving the convex optimization problem. The experimental results on UCI benchmark datasets and artificial datasets demonstrate that compared with other classification models based on SVM, the model proposed in this paper can improve the classification accuracy by about 10%.