On using derivatives and multiple kernel methods for clustering and classifying functional data

In this paper, we propose a framework for rich representation of smooth functional data, leveraging a multiview approach that considers functions and their derivatives as complementary sources of information. Additionally, motivated by the non-linear nature of functional data, we advocate for kernel methods as a suitable modeling approach. We extend existing multiple kernel learning techniques for multivariate data to handle functional data. In particular, we introduce a general procedure for linearly combining different kernel functions. We apply this framework to both clustering and classification tasks, extending multiple kernel k-means and multiple kernel SVM methods to Sobolev functions in H^q. Our experiments involve both simulated and real-world data, demonstrating the effectiveness of our proposed methods.