SFMD-X: A New Functional Data Classifier Based on Shrinkage Functional Mahalanobis Distance

Abstract

In this article, we propose a novel classification approach for functional data based on a shrinkage estimate of functional Mahalanobis distance. We first introduce a new shrinkage functional Mahalanobis distance (SFMD), by using this new distance, we transform the functional observations into a set of vector-valued pseudo-samples. Furthermore, we adopt some good classification algorithms designed for multivariate data to this pseudo-samples instead of the original functional data. The new approach has advantage of highly flexible and scalable, that is, it can easily combine with any classification algorithm, such as support vector machine, tree-based methods, and neural networks. We demonstrate the performance of the proposed functional classifier through both extensive simulation studies and two real data applications.