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Infinite norm large margin classifier
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DOI：10.1007/s13042-018-0881-y.png)
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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.
Keywords:
Margin
Linear programming
Infinite norm
Support vector machine
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