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.
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Acknowledgement
This work was supported in part by the National Foundation for Distinguished Young Scientists under Grant 31125008, the Scientific Research Foundation for Advanced Talents and Returned Overseas Scholars of Nanjing Forestry University under Grant 163070679, and the National Science Foundation of China under Grants 61101197, 61272220, and 61401214.
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He Yan, A., Qiaolin Ye, B., Ying’an Liu, C., Tian’an Zhang, D. (2016). The GEPSVM Classifier Based on L1-Norm Distance Metric. In: Tan, T., Li, X., Chen, X., Zhou, J., Yang, J., Cheng, H. (eds) Pattern Recognition. CCPR 2016. Communications in Computer and Information Science, vol 662. Springer, Singapore. https://doi.org/10.1007/978-981-10-3002-4_57
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