A kernel-free double well potential support vector machine with applications

Abstract

Abstract As a well-known machine learning technique, support vector machine (SVM) with a kernel function achieves much success in nonlinear binary classification tasks. Recently, some quadratic surface SVM models are proposed and studied by utilizing quadratic surfaces for nonlinear binary separations. In this paper, a kernel-free soft quartic surface SVM model is proposed by utilizing the double well potential function for highly nonlinear binary classification. Mathematical analysis on the theoretical properties of the proposed model, including the existence, uniqueness and support vector representation of optimal solutions, is shown. The sequential minimal optimization algorithm is adopted to implement the proposed model for computational efficiency. Numerical results on some artificial and public benchmark data sets demonstrate its effectiveness over well-known SVM models with or without kernel functions. The proposed model is extended to successfully handle some real-life corporate and personal credit data sets for applications.