Nonparallel hyperplane support vector machine for binary classification problems

In this paper, we propose a nonparallel hyperplane support vector machine (NHSVM) for binary classification problems. Our proposed NHSVM is formulated by clustering the training points according to the similarity between classes. It constructs two nonparallel hyperplanes simultaneously by solving a single quadratic programming problem, and is consistent between its predicting and training processes - an essential difference that distinguishes it from other nonparallel SVMs. This proposed NHSVM has been analyzed theoretically and implemented experimentally. The results of experiments conducted using it on both artificial and publicly available benchmark datasets confirm its feasibility and efficacy, especially for “Cross Planes” datasets and datasets with heteroscedastic noise.