Capped L-norm metric based robust least squares twin support vector machine for pattern classification.

Least squares twin support vector machine (LSTSVM) is an effective and efficient learning algorithm for pattern classification. However, the distance in LSTSVM is measured by squared L-norm metric that may magnify the influence of outliers. In this paper, a novel robust least squares twin support vector machine framework is proposed for binary classification, termed as CL-LSTSVM, which utilizes capped L-norm distance metric to reduce the influence of noise and outliers. The goal of CL-LSTSVM is to minimize the capped L-norm intra-class distance dispersion, and eliminate the influence of outliers during training process, where the value of the metric is controlled by the capped parameter, which can ensure better robustness. The proposed metric includes and extends the traditional metrics by setting appropriate values of p and capped parameter. This strategy not only retains the advantages of LSTSVM, but also improves the robustness in solving a binary classification problem with outliers. However, the nonconvexity of metric makes it difficult to optimize. We design an effective iterative algorithm to solve the CL-LSTSVM. In each iteration, two systems of linear equations are solved. Simultaneously, we present some insightful analyses on the computational complexity and convergence of algorithm. Moreover, we extend the CL-LSTSVM to nonlinear classifier and semi-supervised classification. Experiments are conducted on artificial datasets, UCI benchmark datasets, and image datasets to evaluate our method. Under different noise settings and different evaluation criteria, the experiment results show that the CL-LSTSVM has better robustness than state-of-the-art approaches in most cases, which demonstrates the feasibility and effectiveness of the proposed method.