DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classification

Abstract: Functional data - observations in the form of curves or trajectories - arise in diverse domains such as biomedical sensing, motion capture, and handwriting recognition. A core challenge in functional data analysis (FDA) is accounting for phase variability, where misaligned temporal patterns hinder accurate inference. We introduce DeepFRC, an end-to-end deep learning framework for joint functional registration and classification. Unlike conventional approaches that decouple alignment and prediction, DeepFRC integrates class-aware elastic warping and a learnable basis representation into a unified architecture. This design enables temporal alignment and dimensionality reduction to be jointly optimized with classification, improving both interpretability and accuracy. We establish the first theoretical connection between alignment quality and generalization error, and validate our model on synthetic and real-world benchmarks. DeepFRC consistently outperforms state-of-the-art methods, especially in scenarios with complex temporal misalignment. Code is available at: https://github.com/Drivergo-93589/DeepFRC.