  Twin support vector machine (TSVM) is a very classical and practical
classifier for pattern classification. However, the traditional TSVM has two
limitations. Firstly, it uses the L_2-norm distance metric that leads to its
sensitivity to outliers. Second, it needs to select the appropriate kernel
function and the kernel parameters for nonlinear classification. To effectively
avoid these two problems, this paper proposes a robust capped L_1-norm
kernel-free quadratic surface twin support vector machine (CL_1QTSVM). The
strengths of our model are briefly summarized as follows. 1) The robustness of
our model is further improved by employing the capped L_1 norm distance metric.
2) Our model is a kernel-free method that avoids the time-consuming process of
selecting appropriate kernel functions and kernel parameters. 3) The
introduction of L_2-norm regularization term to improve the generalization
ability of the model. 4) To efficiently solve the proposed model, an iterative
algorithm is developed. 5) The convergence, time complexity and existence of
locally optimal solutions of the developed algorithms are further discussed.
Numerical experiments on numerous types of datasets validate the classification
performance and robustness of the proposed model.
