Sparse and robust least squares support vector machine: A linear programming formulation

Least squares support vector machine (LS-SVM) has an outstanding advantage of lower computational complexity than that of standard support vector machines. Its shortcomings are the loss of sparseness and robustness. Thus it usually results in slow testing speed and poor generalization performance. In this paper, a least squares support vector machine with linear programming formulation (LS-SVM-LP) is proposed to deal with above shortcomings. This method is equivalent to solve a linear equation set with deficient rank just like the over complete problem in independent component analysis (ICA). A minimum of 1-norm based object function is chosen to get the sparse and robust solution based on the idea of basis pursuit (BP) in the whole feasible region. Some UCI datasets are used to demonstrate the effectiveness of this model. The experimental results show that LS-SVM-LP can obtain a small number of support vectors and improve the generalization ability of LS-SVM.