Structured sparse support vector machine with ordered features

Kuangnan Fang, Peng Wang, Xiaochen Zhang and Qingzhao Zhang

Journal of Applied Statistics, 2022, vol. 49, issue 5, 1105-1120

Abstract: In the application of high-dimensional data classification, several attempts have been made to achieve variable selection by replacing the $ \ell _{2} $ ℓ2-penalty with other penalties for the support vector machine (SVM). However, these high-dimensional SVM methods usually do not take into account the special structure among covariates (features). In this article, we consider a classification problem, where the covariates are ordered in some meaningful way, and the number of covariates p can be much larger than the sample size n. We propose a structured sparse SVM to tackle this type of problems, which combines the non-convex penalty and cubic spline estimation procedure (i.e. penalizing second-order derivatives of the coefficients) to the SVM. From a theoretical point of view, the proposed method satisfies the local oracle property. Simulations show that the method works effectively both in feature selection and classification accuracy. A real application is conducted to illustrate the benefits of the method.

Date: 2022
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DOI: 10.1080/02664763.2020.1849053

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