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

TL;DR

NeuralFLoC is an unsupervised deep learning framework that jointly registers and clusters functional data using neural ODEs and spectral clustering, achieving state-of-the-art results.

Contribution

It introduces a fully end-to-end neural model for simultaneous registration and clustering of functional data, with theoretical guarantees and robustness.

Findings

State-of-the-art registration and clustering performance.

Robust to missing data, irregular sampling, and noise.

Scalable to large datasets.

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 https://anonymous.4open.science/r/NeuralFLoC-FEC8.