Automatic Feature Scaling and Selection for Support Vector Machine Classi cation with Functional Data

Abstract

Functional Data Analysis (FDA) has become a very important eld in recent years due to its wide range of applications. However, there are several real-life applications in which hybrid functional data appear, i.e., data with functional and static covariates. The classi cation of such hybrid functional data is a challenging problem that can be handled with the Support Vector Machine (SVM). Moreover, the selection of the most informative features may yield to drastic improvements in the classi cation rates. In this paper, an embedded feature selection approach for SVM classi cation is proposed, in which the isotropic Gaussian kernel is modi ed by associating a bandwidth to each feature. The bandwidths are jointly optimized with the SVM parameters, yielding an alternating optimization approach. The e ectiveness of our methodology was tested on benchmark data sets. Indeed, the proposed method achieved the best average performance when compared to 17 other feature selection and SVM classi cation approaches. A comprehensive sensitivity analysis of the parameters related to our proposal was also included, con rming its robustness.