Robust twin depth support vector machine based on average depth

Abstract

As one of the classical machine learning algorithms, twin support vector machine (TWSVM) can construct two nonparallel hyperplanes, which keeps the hyperplane close to points of one class, but far away from the other class. Being different from the classical SVM algorithm, TWSVM can reduce the computational complexity by replacing one large quadratic programming problems (QPPs) with a pair of smaller ones. Although compared to SVM classifier, TWSVM is four times faster, it is still insufficient in resisting noise or outliers. In this paper, we propose a twin depth support vector machine (TDSVM), a binary SVM classifier that considers the influence of depth when calculating the distance. A novel average depth is proposed and applied on TWSVM to construct a robust SVM framework, which can identify outliers in the dataset.By strengthening the center and weakening the edge, a better generalization performance is achieved, and the SRM principle is also implemented. TDSVM can be applied to any place where TWSVM can be applied, which is also useful for reducing the influence of outliers or noise on data and obtaining more robust results. Finally, the advantages of the method are verified theoretically and empirically by experiments. Experimental results on eight UCI datasets and one synthetic dataset demonstrate the effectiveness and robustness of TDSVM. The classification accuracy of TDSVM is better than other compared algorithms on almost every dataset, whether a certain percentage of Gaussian noise is introduced or not.