  Twin support vector machine~(TSVM) is a powerful learning algorithm by
solving a pair of smaller SVM-type problems. However, there are still some
specific issues such as low efficiency and weak robustness when it is faced
with some real applications. In this paper, we propose a Fast and Robust
TSVM~(FR-TSVM) to deal with the above issues. In order to alleviate the effects
of noisy inputs, we propose an effective fuzzy membership function and
reformulate the TSVMs such that different input instances can make different
contributions to the learning of the separating hyperplanes. To further speed
up the training procedure, we develop an efficient coordinate descent algorithm
with shirking to solve the involved a pair of quadratic programming problems
(QPPs). Moreover, theoretical foundations of the proposed model are analyzed in
details. The experimental results on several artificial and benchmark datasets
indicate that the FR-TSVM not only obtains a fast learning speed but also shows
a robust classification performance. Code has been made available at:
https://github.com/gaobb/FR-TSVM.
