Sparse pinball twin support vector machines

The original twin support vector machine (TWSVM) formulation works by solving two smaller quadratic programming problems (QPPs) as compared to the traditional hinge-loss SVM (C-SVM) which solves a single large QPP — this makes the TWSVM training and testing process faster than the C-SVM. However, these TWSVM problems are based on the hinge-loss function and, hence, are sensitive to feature noise and unstable for re-sampling. The pinball-loss function, on the other hand, maximizes quantile distances which grants noise insensitivity but this comes at the cost of losing sparsity by penalizing correctly classified samples as well. To overcome the limitations of TWSVM, we propose a novel sparse pinball twin support vector machines (SPTWSVM) based on the ϵ-insensitive zone pinball loss function to rid the original TWSVM of its noise insensitivity and ensure that the resulting TWSVM problems retain sparsity which makes computations relating to predictions just as fast as the original TWSVM. We further investigate the properties of our SPTWSVM including sparsity, noise insensitivity, and time complexity. Exhaustive testing on several benchmark datasets demonstrates that our SPTWSVM is noise insensitive, retains sparsity and, in most cases, outperforms the results obtained by the original TWSVM.