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

Guo, Xiaohan; Kurtek, Sebastian; Bharath, Karthik


Xiaohan Guo

Sebastian Kurtek


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.


Guo, X., Kurtek, S., & Bharath, K. (2022). Variograms for kriging and clustering of spatial functional data with phase variation. Spatial Statistics, 51, Article 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
Keywords Management, Monitoring, Policy and Law; Computers in Earth Sciences; Statistics and Probability
Public URL
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