Mixtures of spatial factor analyzers for tensor-variate data
Abstract
A mixture of spatial factor analyzers (MSFA) is introduced to address the challenges of clustering high-dimensional spatial data. The proposed framework utilizes the given coordinate system to implement a flexible, spline-based spatial decay covariance structure. In this approach, the number of covariance parameters increases linearly with the number of spatial locations, rather than increasing quadratically. To model non-spatial dependence, matrix variate factor analyzers are employed for further dimensionality reduction. Parameter estimation is conducted via a variant of the expectation-maximization algorithm combined with a generalized least squares estimator. The proposed models are explored in the context of tensor-variate data analysis, where simulation studies and three applications---Raman spectroscopy, SpecTex hyperspectral textures, and the Salinas hyperspectral scene---illustrate their ability to recover and distinguish spatial dependence patterns. The R implementation is available on CRAN: https://CRAN.R-project.org/package=SpatMix.
Related
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BibTeX
@misc{lu2026mixtures,
title = {{Mixtures of spatial factor analyzers for tensor-variate data}},
author = {Hanzhang Lu and Keiran Malott and Kirsty Milligan and Sanjeena Subedi and Edana Cassol and Vinita Chauhan and Connor McNairn and Prarthana Pasricha and Sangeeta Murugkar and Rowan M. Thomson and Andrew Jirasek and Jeffrey L. Andrews},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.07887},
eprint = {2607.07887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07887},
}
RIS
TY - UNPB
TI - Mixtures of spatial factor analyzers for tensor-variate data
AU - Hanzhang Lu
AU - Keiran Malott
AU - Kirsty Milligan
AU - Sanjeena Subedi
AU - Edana Cassol
AU - Vinita Chauhan
AU - Connor McNairn
AU - Prarthana Pasricha
AU - Sangeeta Murugkar
AU - Rowan M. Thomson
AU - Andrew Jirasek
AU - Jeffrey L. Andrews
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2607.07887
UR - https://arxiv.org/abs/2607.07887
AB - A mixture of spatial factor analyzers (MSFA) is introduced to address the challenges of clustering high-dimensional spatial data. The proposed framework utilizes the given coordinate system to implement a flexible, spline-based spatial decay covariance structure. In this approach, the number of covariance parameters increases linearly with the number of spatial locations, rather than increasing quadratically. To model non-spatial dependence, matrix variate factor analyzers are employed for further dimensionality reduction. Parameter estimation is conducted via a variant of the expectation-maximization algorithm combined with a generalized least squares estimator. The proposed models are explored in the context of tensor-variate data analysis, where simulation studies and three applications---Raman spectroscopy, SpecTex hyperspectral textures, and the Salinas hyperspectral scene---illustrate their ability to recover and distinguish spatial dependence patterns. The R implementation is available on CRAN: https://CRAN.R-project.org/package=SpatMix.
ER -