A kernel-free fuzzy support vector machine with Universum

Support vector machines with Universum are attractive for dealing with classification problems by incorporating prior information. In this paper, a quadratic function based kernel-free support vector machine with Universum is proposed for binary classification. To deal with noise and outliers, two fuzzy membership functions considering both information entropy and distance information are constructed for labeled and Universum data, respectively. The fuzzy membership function for Universum is also adopted for further selecting Universum data to improve the robustness. The proposed model corresponds to an efficiently solved convex quadratic programming. In the meanwhile, by avoiding the issue of choosing kernel functions, the proposed model saves more computational time when compared with other Universum-based support vector machines. Finally, some numerical tests are implemented on several data sets to validate the classification effectiveness of the proposed method. The numerical results illustrate the competitive performance when compared with some state-of-the-art support vector machines. Applications on two credit rating data sets are also conducted to distinguish the classification performance of the proposed method.