Robust Nonparallel Support Vector Machines via Second-Order Cone Programming

Abstract A novel binary classification approach is proposed in this paper, extending the ideas behind nonparallel support vector machine (NPSVM) to robust machine learning. NPSVM constructs two twin hyperplanes by solving two independent quadratic programming problems and generalizes the well-known twin support vector machine (TWSVM) method. Robustness is conferred on the NPSVM approach by using a probabilistic framework for maximizing model fit, which is cast into two second-order cone programming (SOCP) problems by assuming a worst-case setting for the data distribution of the training patterns. Experiments on benchmark datasets confirmed the theoretical virtues of our approach, showing superior average performance compared with various SVM formulations.