Support vector machine classifiers by non-Euclidean margins.

In this article, the classical support vector machine (SVM) classifiers are generalized by the non-Euclidean margins. We first extend the linear models of the SVM classifiers by the non-Euclidean margins including the theorems and algorithms of the SVM classifiers by the hard margins and the soft margins. Specially, the SVM classifiers by the -norm margins can be solved by the 1-norm optimization with sparsity. Next, we show that the non-linear models of the SVM classifiers by the -norm margins can be equivalently transferred to the SVM in the -norm reproducing kernel Banach spaces given by the hinge loss, where. Finally, we illustrate the numerical examples of artificial data and real data to compare the different algorithms of the SVM classifiers by the -norm margin. [ABSTRACT FROM AUTHOR]