Simultaneous Registration and Clustering for Multi-dimensional Functional Data

TL;DR

This paper introduces a novel simultaneous registration and clustering (SRC) model for multi-dimensional functional data that incorporates both functional and scalar variables, improving group identification and data alignment.

Contribution

The proposed SRC model uniquely combines registration and clustering in a two-level framework, utilizing Gaussian process regression and scalar variable-based allocation, which is novel in functional data analysis.

Findings

Effective on simulated data

Successfully applied to real data

Improves clustering accuracy

Abstract

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.