A Class of Fuzzy Smooth Piecewise Twin Support Vector Machine

Abstract

In order to improve the classification ability of the Twin Support Vector Machine (TWSVM), a new class of twice continuously differentiable piecewise smooth functions is used to smooth the objective function of unconstrained TWSVM and a class of smooth piecewise twin support vector machine (SPTWSVMd) is proposed. It is shown that the approximation accuracy and smoothness rank of piecewise functions can be as high as required. In order to reduce the influence of noise, the membership function is defined according to the distance between the sample points of each class and its intra-class hyperplane and a class of fuzzy SPTWSVMd (FSPTWSVMd) is proposed. The FSPTWSVMd can efficiently handle large scale and high dimensional problems based on the reduced kernel technique. The effectiveness of the proposed method is demonstrated via experiments on NDC datasets.