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Infinite norm large margin classifier

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Abstract

Standard support vector machine (SVM) achieves good generalization by maximizing margin and the leading optimization problem can be solved by quadratic programming (QP). Geometrically, such margin description benefits from closed-formed Euclidian distance formula between the support vectors to the decision plane (point-to-plane) based on L2 norm. However, for non-L2 norm learning machines, such as L1- or infinite-norm, due to their non-differentiability, it is difficult to obtain close-formed point-to-plane distance and thus rarely seen large margin classifiers based on other norms in literatures. In this paper, we proposed an infinite-norm large margin classifier, termed as InfLMC. Firstly, for any given points and a plane, the foresaid close-formed distance and projection formula, based on infinite nom, are mathematically described, and then, similar to L2-SVM, infinite norm margin can be directly derived. Thus, the proposed InfLMC is constructed by maximizing margin and simultaneously minimizing experience error. Furthermore, the leading optimization problem can be solved by a linear programming problem (LP) rather than QP in standard SVM. Finally, the experimental results on some artificial and UCI datasets show its performance in test correctness and running time-consume.

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Acknowledgements

We thank the anonymous reviewers for their valuable comments and suggestions. This research was supported by Central Public-interest Scientific Institution Basal Research Fund (Grant No.CAFYBB2016SZ003), Natural Science Foundation of China (31670554 and 61871444), and the Jiangsu Science Foundation (BK20161527 and BK20171453).

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Authors and Affiliations

  1. College of Information Science and Technology, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Hongxin Yang, Xubing Yang, Fuquan Zhang, Qiaolin Ye & Xijian Fan

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  1. Hongxin Yang
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  2. Xubing Yang
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Correspondence to Xubing Yang.

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Yang, H., Yang, X., Zhang, F. et al. Infinite norm large margin classifier. Int. J. Mach. Learn. & Cyber. 10, 2449–2457 (2019). https://doi.org/10.1007/s13042-018-0881-y

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