Spatially penalized registration of multivariate functional data

Guo, Xiaohan; Kurtek, Sebastian; Bharath, Karthik

Abstract

Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the hitherto unconsidered setting where phase variation of the component functions are spatially correlated. We propose an algorithm to optimize a metric-based objective function for registration with a novel penalty term that incorporates the spatial correlation between the component phase variations through a kriging prediction of an appropriate phase random field. The penalty term encourages the overall phase at a particular location to be similar to the spatially weighted average phase in its neighbourhood, and thus engenders a regularization that prevents over-alignment. Utility of the registration method, and its superior performance compared to methods that fail to account for the spatial correlation, is demonstrated through performance on simulated examples and two multivariate functional datasets pertaining to electroencephalogram signals and ozone concentration functions. The generality of the framework opens up the possibility for extension to settings involving different forms of correlation between the component functions and their phases.

Citation

Guo, X., Kurtek, S., & Bharath, K. (2023). Spatially penalized registration of multivariate functional data. Spatial Statistics, 56, Article 100760. https://doi.org/10.1016/j.spasta.2023.100760

• Journal Article Type: Article
• Acceptance Date: Jun 7, 2023
• Online Publication Date: Jun 22, 2023
• Publication Date: Aug 1, 2023
• Deposit Date: Jun 19, 2023
• Publicly Available Date: Jun 23, 2024
• Journal: Spatial Statistics
• Print ISSN: 2211-6753
• Electronic ISSN: 2211-6753
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 56
• Article Number: 100760
• DOI: https://doi.org/10.1016/j.spasta.2023.100760
• Keywords: Elastic metric; Functional random field; Phase trace-variogram; Warping invariance
• Public URL: https://nottingham-repository.worktribe.com/output/22143427
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S2211675323000350?via%3Dihub