Tree-Based Classification of High-Dimensional Functional Data via Feature Enrichment

This paper addresses supervised classification of functional data by proposing a structured functional feature enrichment framework, aimed at improving predictive performance through enhanced functional representations and designed to be integrated into existing classification methods. Functional observations are represented using a B-spline basis system, fixed across training and test sets to ensure coherence, but selected in a flexible, data-driven manner through cross-validation on the training data. Starting from the original curves, the feature space is enriched by including first and second derivatives, curvature, radius of curvature, and elasticity, allowing classifiers to capture complementary geometric and dynamic characteristics of the data. The enrichment process is formulated in a structured and reproducible way, enabling explicit control over the contribution of each functional transformation. The proposed framework is coupled with several classification methods, including Functional Classification Trees, Functional K-Nearest Neighbors, Functional Random Forests, Functional XGBoost, and Functional LightGBM. Extensive experiments on seven benchmark datasets, commonly used in the functional and time series classification literature, show that feature enrichment can improve classification accuracy and reduce variability when coupled with classifiers able to exploit heterogeneous and partially redundant functional descriptors, particularly ensemble-based methods. At the same time, the results also show that enrichment is not uniformly beneficial across classifiers and datasets, and may be detrimental for distance-based methods. Issues related to interpretability, explainability, and computational cost are also investigated, providing a comprehensive evaluation of when and why the proposed enrichment framework is useful in supervised functional classification.