Automatic feature scaling and selection for support vector machine classification with functional data

FunctionalData Analysis (FDA) has become a very important field 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 classification 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 classification rates. In this paper, an embedded feature selection approach for SVM classification is proposed, in which the isotropic Gaussian kernel is modified by associating a bandwidth to each feature. The bandwidths are jointly optimized with the SVM parameters, yielding an alternating optimization approach. The effectiveness 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 classification approaches. A comprehensive sensitivity analysis of the parameters related to our proposal was also included, confirming its robustness.