[2602.03169] NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data

Statistics > Machine Learning arXiv:2602.03169 (stat) [Submitted on 3 Feb 2026 (v1), last revised 29 Apr 2026 (this version, v2)] Title:NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data Authors:Xinyang Xiong, Siyuan jiang, Pengcheng Zeng View a PDF of the paper titled NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data, by Xinyang Xiong and 2 other authors View PDF HTML (experimental) Abstract:Clustering functional data in the presence of phase variation is challenging, as temporal misalignment can obscure intrinsic shape differences and degrade clustering performance. Most existing approaches treat registration and clustering as separate tasks or rely on restrictive parametric assumptions. We present \textbf{NeuralFLoC}, a fully unsupervised, end-to-end deep learning framework for joint functional registration and clustering based on Neural ODE-driven diffeomorphic flows and spectral clustering. The proposed model learns smooth, invertible warping functions and cluster-specific templates simultaneously, effectively disentangling phase and amplitude variation. We establish universal approximation guarantees and asymptotic consistency for the proposed framework. Experiments on functional benchmarks show state-of-the-art performance in both registration and clustering, with robustness to missing data, irregular sampling, and noise, while maintaining scalability. Code is available at this https URL. Subjects: Mac...