NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data
This addresses the challenge of functional data analysis for researchers and practitioners, offering a robust and scalable solution, though it is incremental as it builds on existing neural ODE and spectral clustering methods.
The paper tackled the problem of clustering functional data with phase variation by introducing NeuralFLoC, a deep learning framework for joint registration and clustering, which achieved state-of-the-art performance in both tasks on functional benchmarks.
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 https://anonymous.4open.science/r/NeuralFLoC-FEC8.