用神经流统一处理功能数据配准与聚类，提升形状分析精度。
NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data
- 基于神经微分方程构建可逆形变流，同时学习时间对齐与聚类模板。
- 在多个基准数据集上实现最优配准与聚类效果，对噪声和缺失数据鲁棒。
- 无需参数假设，适合不规则采样或带噪声的功能数据分析场景。
在存在相位变异的情况下对功能数据进行聚类极具挑战性，因为时间错位会掩盖内在形状差异，降低聚类性能。现有方法通常将配准与聚类分开处理，或依赖严格参数假设。本文提出 extbf{NeuralFLoC}，一种全无监督、端到端的深度学习框架，结合神经微分方程驱动的保角流与谱聚类，实现功能数据的联合配准与聚类。该模型可同时学习平滑、可逆的扭曲函数与各簇特异的模板，有效分离相位与振幅变异。我们建立了该框架的通用逼近保证与渐近一致性。在功能数据基准测试中，模型在配准与聚类任务上均达到当前最佳性能，对缺失数据、不规则采样和噪声具有强鲁棒性，同时保持良好可扩展性。代码已公开于 https://anonymous.4open.science/r/NeuralFLoC-FEC8。
原文摘要 · Abstract (English)
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.
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