Feature Selection via l _p -Norm Support Vector Machines

Abstract

Though support vector machine has been a promising tool in machine learning, but it does not directly obtain the feature importance. Identifying a subset of features which contribute most to classification is also an important task in classification. The benefit of feature selection is twofold. It leads to parsimonious models that are often preferred in many scientific problems, and it is also crucial for achieving good classification accuracy in the presence of redundant features. We can combine SVM with various feature selection strategies. Some of them are “filters”: general feature selection methods independent of SVM; on the other hand, some are wrapper-type methods: modifications of SVM which choose important features as well as conduct training/testing. In the machine learning literature, there are several proposals for feature selection to accomplish the goal of automatic feature selection in the SVM, in some of which they applied the l ₀-norm, l ₁-norm SVM and got competitive performance. We proposed two models in this chapter, l _p -norm C-support vector classification (l _p -SVC) and l _p -norm proximal support vector machine (l _p -PSVM), which separately combines C-SVC and PSVM with feature selection strategy by introducing the l _p -norm (0<p<1).