A normal least squares support vector machine (NLS-SVM) and its learning algorithm

Least squares support vector machine (LS-SVM) is a successful method for classification or regression problems, in which the margin and sum square errors (SSEs) on training samples are simultaneously minimized. However, LS-SVM only considers the SSEs of input variable. In this paper, a novel normal least squares support vector machine (NLS-SVM) is proposed, which effectively considers the noises on both input and response variables. It introduces a two-stage learning method to solve NLS-SVM. More importantly, a fast iterative updating algorithm is presented, which reaches the solution of NLS-SVM with lower computational complexity instead of directly adopting the two-stage learning method. Several experiments on artificial and real-world datasets are simulated, in which the results show that NLS-SVM outperforms LS-SVM.