Capped [formula omitted]-norm metric based robust least squares twin support vector machine for pattern classification

Abstract

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 L2-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 CL2,p-LSTSVM, which utilizes capped L2,p-norm distance metric to reduce the influence of noise and outliers. The goal of CL2,p-LSTSVM is to minimize the capped L2,p-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 CL2,p-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 CL2,p-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 CL2,p-LSTSVM has better robustness than state-of-the-art approaches in most cases, which demonstrates the feasibility and effectiveness of the proposed method.