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

arXiv: https://arxiv.org/abs/2602.03169 · HTML: https://mlsanity.com/paper/2602.03169/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 13 of 13)

- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Universal Approximation Property of Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.02414/) (2020)
- [Functional Data Analysis of Amplitude and Phase Variation](https://mlsanity.com/paper/1512.03216/) (2015)
- [Functional Autoencoder for Smoothing and Representation Learning](https://mlsanity.com/paper/2401.09499/) (2024)
- [Simultaneous Registration and Clustering for Multi-dimensional Functional Data](https://mlsanity.com/paper/1711.04761/) (2017)
- [Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data](https://mlsanity.com/paper/1912.05125/) (2019)
- [DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classification](https://mlsanity.com/paper/2501.18116/) (2025)
- [Review of Functional Data Analysis](https://mlsanity.com/paper/1507.05135/) (2015)
- [Adaptively Truncated Signature-based Logistic Regression for Semi-parametric Functional Classification](https://mlsanity.com/paper/2507.06637/) (2025)
- [RandomNet: Clustering Time Series Using Untrained Deep Neural Networks](https://mlsanity.com/paper/2408.07956/) (2024)

## Built on by (most cited first, 1 of 1)

- [Functional Autoencoders for Amplitude-Phase Representation Learning](https://mlsanity.com/paper/2609.34207/) (2026)

## Abstract (arXiv)

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 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.