Linear support vector machines with normalizations

In this paper, we start with the standard support vector machine (SVM) formulation and extend it by proposing a general SVM that allows many different variations captured by normalizations in the formulation with very diverse numerical performance. The proposed formulation can not only capture the existing work, i.e., standard soft-margin SVM, ℓ₁-SVM, as special cases, but also enable us to propose more SVMs that outperform the existing ones under some scenarios.