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Multi-task nonparallel support vector machine for classification

Direct multi-task twin support vector machine (DMTSVM) explores the shared information between multiple correlated tasks, then it produces better generalization performance. However, it contains matrix inversion operation when solving the dual problems, so it costs much running time. Moreover, kernel trick cannot be directly utilized in the nonlinear case. To effectively avoid above problems, a novel multi-task nonparallel support vector machine (MTNPSVM) including linear and nonlinear cases is proposed in this paper. By introducing epsilon-insensitive loss instead of square loss in DMTSVM, MTNPSVM effectively avoids matrix inversion operation and takes full advantage of the kernel trick. Theoretical implication of the model is further discussed. To further improve the computational efficiency, the alternating direction method of multipliers (ADMM) is employed when solving the dual problem. The computational complexity and convergence of the algorithm are provided. In addition, the property and sensitivity of the parameter in model are further explored. The experimental results on fifteen benchmark datasets and twelve image datasets demonstrate the validity of MTNPSVM in comparison with the state-of-the-art algorithms. Finally, it is applied to real Chinese Wine dataset, and also verifies its effectiveness.

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