L1-Norm GEPSVM Classifier Based on an Effective Iterative Algorithm for Classification

The proximal support vector machine via generalized eigenvalues (GEPSVM) is an excellent classifier for binary classification problem. However, in conventional GEPSVM the distance is measured by L2-norm, which makes it prone to being affected by the presence of outliers by the square operation. To alleviate this, we propose a robust and effective GEPSVM classification algorithm based on L1-norm distance metric, termed 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 used 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 develop an effective iterative algorithm to solve the L1-norm optimal problems, which is easy to implement and its convergence to a local optimum is theoretically ensured. Thus, the classification performance of L1-GEPSVM is more robust than GEPSVM. Finally, the feasibility and effectiveness of L1-GEPSVM are further verified by extensive experimental results on artificial datasets, UCI datasets and NDC datasets.