DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classification
Journal:
arXiv
Published Date:
Jan 30, 2025
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.
