Least squares twin bounded support vector machines based on L1-norm distance metric for classification. (February 2018) - Yan, He; Ye, Qiaolin; Zhang, Tian'an; Yu, Dong-Jun; Yuan, Xia; Xu, Yiqing; Fu, Liyong
Highlights: We have enhanced TBSVM to LSTBSVM in least squares sense, while in LSTBSVM the distance is measured by L1-norm. L1-LSTBSVM has more robustness to outliers, can lower the computational costs and improve the classification performance. We design a valid iterative algorithm to solve the L1-norm optimal problems, which is an important theoretical contribution. The method which we proposed can be conveniently extended to solve other improved methods of TWSVM. Abstract: In this paper, we construct a least squares version of the recently proposed twin bounded support vector machine (TBSVM) for binary classification. As a valid classification tool, TBSVM attempts to seek two non-parallel planes that can be produced by solving a pair of quadratic programming problems (QPPs), but this is time-consuming. Here, we solve two systems of linear equations rather than two QPPs to avoid this deficiency. Furthermore, the distance in least squares TBSVM (LSTBSVM) is measured by L2-norm, but L1-norm distance is usually regarded as an alternative to L2-norm to improve model robustness in the presence of outliers. Inspired by the advantages of least squares twin support vector machine (LSTWSVM), TBSVM and L1-norm distance, we propose a LSTBSVM based on L1-norm distance metric for binary classification, termed as L1-LSTBSVM, which is specially designed for suppressing the negative effect of outliers and improving computational efficiency in large datasets. Then, we design a powerful iterative algorithm to solve the L1-norm optimal problems, and it is easy to implement and its convergence to an optimum solution is theoretically ensured. Finally, the feasibility and effectiveness of L1-LSTBSVM are validated by extensive experimental results on both UCI datasets and artificial datasets.