Piecewise linear solution path for pinball twin support vector machine

Twin support vector machine with pinball loss (PinTSVM) has been proposed recently, which enjoys noise insensitivity and has many admirable properties. However, users have to repeatedly train the model multiple times to tune parameters. To address this issue, in this paper we propose a new solution-path approach for the PinTSVM (Path-PinTSVM). We prove that both the primal and dual solutions are piecewise linear with the model parameters c and r varying. The proposed algorithm could provide the optimal accuracy through all possible parameter values. The solution for the starting point of the path could be achieved analytically without solving optimization problem. Compared with the existing path algorithms for SVMs, our method is more flexible and has better prediction performance. As it deals with two classes separately, the analytic solution could be directly obtained no matter whether two classes are balanced or not. Besides, the computational cost is also less since only one class of the instances is considered at a time. Our approach also gives a guidance for exploiting path algorithms for other TSVMs. In numerical experiments, the validity of our proposed method is demonstrated on a synthetic dataset, 16 benchmark datasets and a real biological dataset.