Variograms for kriging and clustering of spatial functional data with phase variation

Guo, Xiaohan; Kurtek, Sebastian; Bharath, Karthik

Abstract

Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace-variogram, which quantifies spatial variation, can be misleading when analyzing misaligned functional data with phase variation. To remedy this, we describe a framework that extends amplitude-phase separation methods in functional data to the spatial setting, with a view towards performing clustering and spatial prediction. We propose a decomposition of the trace-variogram into amplitude and phase components, and quantify how spatial correlations between functional observations manifest in their respective amplitude and phase. This enables us to generate separate amplitude and phase clustering methods for spatial functional data, and develop a novel spatial functional interpolant at unobserved locations based on combining separate amplitude and phase predictions. Through simulations and real data analyses, we demonstrate advantages of our approach when compared to standard ones that ignore phase variation, through more accurate predictions and more interpretable clustering results.

Citation

Guo, X., Kurtek, S., & Bharath, K. (2022). Variograms for kriging and clustering of spatial functional data with phase variation. Spatial Statistics, 51, Article 100687. https://doi.org/10.1016/j.spasta.2022.100687

• Journal Article Type: Article
• Acceptance Date: Jun 27, 2022
• Online Publication Date: Jul 20, 2022
• Publication Date: Oct 1, 2022
• Deposit Date: Aug 31, 2022
• Publicly Available Date: Jul 21, 2023
• Journal: Spatial Statistics
• Print ISSN: 2211-6753
• Electronic ISSN: 2211-6753
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Article Number: 100687
• DOI: https://doi.org/10.1016/j.spasta.2022.100687
• Keywords: Management, Monitoring, Policy and Law; Computers in Earth Sciences; Statistics and Probability
• Public URL: https://nottingham-repository.worktribe.com/output/10633218
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S2211675322000525