Neighbourhood-Based Generalized Dynamic Principal Components for Spatial Functional Data
Abstract
Regular-grid spatial functional datasets arise naturally in gridded environmental, oceanographic, climate, and remote-sensing applications, where each spatial location is associated with an entire curve. Existing spectral spatial functional principal component analysis methods provide an important frequency-domain approach for such data, but they do not directly target finite-neighbourhood least-squares reconstruction from an estimated latent spatial component field. To address this, we propose Spatial Functional Generalized Dynamic Principal Components (SFGDPC), a reconstruction-based dimension-reduction method for regular-grid spatial functional data. Each function is first represented by basis coefficients, and each coefficient vector is reconstructed from a scalar latent spatial field and its Chebyshev neighbourhood on the rectangular grid. The spatial neighbourhood radius is selected using a Bayesian information criterion (BIC)-type conditional reconstruction criterion. In the local-neighbourhood transfer simulation, SFGDPC reduced mean cumulative normalized mean squared error (NMSE) relative to spatial functional principal component analysis (SFPCA) by approximately 38-53% across the reported component counts and covariance conditions. In the Indian Ocean sea surface temperature (SST) application, one SFGDPC component produced lower whole-grid reconstruction error than both the boundary-safe and high-cap SFPCA benchmarks across all 33 annual fields. The results support SFGDPC as a local reconstruction-based complement to spectral SFPCA for regular-grid spatial functional data.
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BibTeX
@misc{pathmanathan2026neighbourhoodbased,
title = {{Neighbourhood-Based Generalized Dynamic Principal Components for Spatial Functional Data}},
author = {Dharini Pathmanathan and Teck Xiang Seow and Philipp Otto and Sophie Dabo-Niang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14986},
eprint = {2609.14986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14986},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Neighbourhood-Based Generalized Dynamic Principal Components for Spatial Functional Data
AU - Dharini Pathmanathan
AU - Teck Xiang Seow
AU - Philipp Otto
AU - Sophie Dabo-Niang
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14986
UR - https://arxiv.org/abs/2609.14986
AB - Regular-grid spatial functional datasets arise naturally in gridded environmental, oceanographic, climate, and remote-sensing applications, where each spatial location is associated with an entire curve. Existing spectral spatial functional principal component analysis methods provide an important frequency-domain approach for such data, but they do not directly target finite-neighbourhood least-squares reconstruction from an estimated latent spatial component field. To address this, we propose Spatial Functional Generalized Dynamic Principal Components (SFGDPC), a reconstruction-based dimension-reduction method for regular-grid spatial functional data. Each function is first represented by basis coefficients, and each coefficient vector is reconstructed from a scalar latent spatial field and its Chebyshev neighbourhood on the rectangular grid. The spatial neighbourhood radius is selected using a Bayesian information criterion (BIC)-type conditional reconstruction criterion. In the local-neighbourhood transfer simulation, SFGDPC reduced mean cumulative normalized mean squared error (NMSE) relative to spatial functional principal component analysis (SFPCA) by approximately 38-53% across the reported component counts and covariance conditions. In the Indian Ocean sea surface temperature (SST) application, one SFGDPC component produced lower whole-grid reconstruction error than both the boundary-safe and high-cap SFPCA benchmarks across all 33 annual fields. The results support SFGDPC as a local reconstruction-based complement to spectral SFPCA for regular-grid spatial functional data.
ER -