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

2025-01-30

AI Summary

To address the performance limitations arising from the decoupled treatment of registration and classification in functional data analysis, this paper proposes DeepFRC—a fully end-to-end trainable framework that jointly optimizes elastic time-warping alignment and discriminative feature learning for the first time. Methodologically, DeepFRC introduces a learnable elastic registration module and an adaptive orthogonal basis representation module, enabling differentiable time warping and joint gradient-based optimization; we further provide theoretical guarantees on its low misalignment error and generalization error bound. Extensive experiments on multiple real-world datasets demonstrate that DeepFRC significantly outperforms state-of-the-art methods: it achieves a 12.7% improvement in registration accuracy under strong deformations and high noise, and an average 5.3% gain in classification accuracy—validating the effectiveness and robustness of joint modeling.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

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.

Problem

• Functional Data Analysis
• Data Alignment
• Classification

Innovation

• DeepFRC
• Simultaneous Alignment and Classification
• Enhanced Alignment Accuracy