Twin Hyper-Ellipsoidal Support Vector Machine for Binary Classification

Abstract

In this paper, a twin hyper-ellipsoidal support vector machine (TESVM) for binary classification of data is presented. Similar to twin support SVM(TWSVM) and twin hypersphere SVM (THSVM), as in the literature, our proposed method finds two hyper-ellipsoidals by solving two related SVM-type quadratic programming problem (QPPs), each of which is smaller than that of the classical SVM, causing it to achieve higher speed. The main idea of this paper is to employ Mahalanobis distance-based kernels for two classes of data in the THSVM algorithm to improve its generalization performance. Since the kernel used in SVM, TWSVM, and THSVM is based on Euclidean distance, it is assumed that the data points have been distributed in a hyper-spherical region, while the data points of two classes have been distributed in two different hyper-ellipsoidal regions. As mentioned in the literature, to work with hyper-ellipsoidal areas, Mahalanobis distance is a better choice than Euclidean distance. The effect of computational results of SVM, TWSVM, THSVM, and TESVM in terms of generalization performance and central processing unit (CPU) learning time on several benchmarks as well as synthetic and image datasets indicates, TESVM achieves fast learning speed along with higher generalization.