A new fuzzy support vector machine with pinball loss

Abstract

Abstract The fuzzy support vector machine (FSVM) assigns each sample a fuzzy membership value based on its relevance, making it less sensitive to noise or outliers in the data. Although FSVM has had some success in avoiding the negative effects of noise, it uses hinge loss, which maximizes the shortest distance between two classes and is ineffective in dealing with feature noise near the decision boundary. Furthermore, whereas FSVM concentrates on misclassification errors, it neglects to consider the critical within-class scatter minimization. We present a Fuzzy support vector machine with pinball loss (FPin-SVM), which is a fuzzy extension of a reformulation of a recently proposed support vector machine with pinball loss (Pin-SVM) with several significant improvements, to improve the performance of FSVM. First, because we used the squared L2- norm of errors variables instead of the L1 norm, our FPin-SVM is a strongly convex minimization problem; second, to speed up the training procedure, solutions of the proposed FPin-SVM, as an unconstrained minimization problem, are obtained using the functional iterative and Newton methods. Third, it is proposed to solve the minimization problem directly in primal. Unlike FSVM and Pin-SVM, our FPin-SVM does not require a toolbox for optimization. We dig deeper into the features of FPin-SVM, such as noise insensitivity and within-class scatter minimization. We conducted experiments on synthetic and real-world datasets with various sounds to validate the usefulness of the suggested approach. Compared to the SVM, FSVM, and Pin-SVM, the presented approaches demonstrate equivalent or superior generalization performance in less training time.

Keywords

• Hinge loss
• Pinball loss
• Support vector machine
• Fuzzy support vector machine