  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.
