The GEPSVM classifier based on L1-norm distance metric

Abstract

The proximal support vector machine via generalized eigenvalues (GEPSVM) is an excellent classifier for binary classification problem. However, the distance of GEPSVM from the point to the plane is measured by L2-norm, which emphasizes the role of outliers by the square operation. To optimize this, we propose a robust and effective GEPSVM classifier based on L1-norm distance metric, referred to as L1-GEPSVM. The optimization goal is to minimize the intra-class distance dispersion and maximize the inter-class distance dispersion simultaneously. It is known that the application of L1-norm distance is often considered as a simple and powerful way to reduce the impact of outliers, which improves the generalization ability and flexibility of the model. In addition, we design an effective iterative algorithm to solve the L1-norm optimal problems, which is easy to actualize and its convergence to a logical local optimum is theoretically ensured. Thus, the classification performance of L1-GEPSVM is more robust. Finally, the feasibility and effectiveness of L1-GEPSVM are proved by extensive experimental results on both UCI datasets and artificial datasets.