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

2026-02-03

AI Summary

This work addresses the degradation of clustering performance in functional data caused by phase variation obscuring true shape differences. It proposes the first end-to-end unsupervised deep learning framework that jointly optimizes registration and clustering. By coupling neural ordinary differential equation (Neural ODE)-driven diffeomorphic flows with spectral clustering, the method simultaneously estimates smooth, invertible warping functions and cluster-specific templates, effectively disentangling phase and amplitude variations. Theoretical analysis establishes the model’s universal approximability and asymptotic consistency, overcoming limitations of traditional approaches that rely on parametric assumptions or sequential processing. Experiments demonstrate state-of-the-art performance across multiple benchmarks, with strong robustness to missing data, non-uniform sampling, and noise, as well as favorable scalability.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• functional data clustering
• phase variation
• temporal misalignment
• amplitude variation
• joint registration

Innovation

• Neural ODE
• diffeomorphic flow
• functional data clustering
• joint registration and clustering
• phase-amplitude separation