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

Functional data analysis (FDA) is essential for analyzing continuous, high-dimensional data, yet existing methods often decouple functional registration and classification, limiting their efficiency and performance. We present DeepFRC, an end-to-end deep learning framework that unifies these tasks within a single model. Our approach incorporates an alignment module that learns time warping functions via elastic function registration and a learnable basis representation module for dimensionality reduction on aligned data. This integration enhances both alignment accuracy and predictive performance. Theoretical analysis establishes that DeepFRC achieves low misalignment and generalization error, while simulations elucidate the progression of registration, reconstruction, and classification during training. Experiments on real-world datasets demonstrate that DeepFRC consistently outperforms state-of-the-art methods, particularly in addressing complex registration challenges. Code is available at: https://github.com/Drivergo-93589/DeepFRC.