# Simultaneous Registration and Clustering for Multi-dimensional Functional Data

arXiv: https://arxiv.org/abs/1711.04761 · HTML: https://mlsanity.com/paper/1711.04761/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2017.

## Built on by (most cited first, 4 of 4)

- [Review of Clustering Methods for Functional Data](https://mlsanity.com/paper/2210.00847/) (2022)
- [Nonparametric Multi-shape Modeling with Uncertainty Quantification](https://mlsanity.com/paper/2206.09127/) (2022)
- [NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data](https://mlsanity.com/paper/2602.03169/) (2026)
- [Functional Autoencoders for Amplitude-Phase Representation Learning](https://mlsanity.com/paper/2609.34207/) (2026)

## Abstract (arXiv)

The clustering for functional data with misaligned problems has drawn much attention in the last decade. Most methods do the clustering after those functional data being registered and there has been little research using both functional and scalar variables. In this paper, we propose a simultaneous registration and clustering (SRC) model via two-level models, allowing the use of both types of variables and also allowing simultaneous registration and clustering. For the data collected from subjects in different unknown groups, a Gaussian process functional regression model with time warping is used as the first level model; an allocation model depending on scalar variables is used as the second level model providing further information over the groups. The former carries out registration and modeling for the multi-dimensional functional data (2D or 3D curves) at the same time. This methodology is implemented using an EM algorithm, and is examined on both simulated data and real data.