Spatial Covariance Constraints for Gaussian Mixture Models
Abstract
Although extensive research exists in spatial modeling, few studies have addressed finite mixture model-based clustering methods for spatial data. Finite mixture models, especially Gaussian mixture models, particularly suffer from high dimensionality due to the number of free covariance parameters. This study introduces a spatial covariance constraint for Gaussian mixture models that requires only four free parameters for each component, independent of dimensionality. Using a coordinate system, the spatially constrained Gaussian mixture model enables clustering of multi-way spatial data and inference of spatial patterns. The parameter estimation is conducted by combining the expectation-maximization (EM) algorithm with the generalized least squares (GLS) estimator. Simulation studies and applications to Raman spectroscopy data are provided to demonstrate the proposed model.
Cite
@article{arxiv.2601.07979,
title = {Spatial Covariance Constraints for Gaussian Mixture Models},
author = {Hanzhang Lu and Keiran Malott and Venkat Suprabath Bitra and Kirsty Milligan and Sanjeena Subedi and Edana Cassol and Vinita Chauhan and Connor McNairn and Bryan Muir and Prarthana Pasricha and Sangeeta Murugkar and Rowan Thomson and Andrew Jirasek and Jeffrey L. Andrews},
journal= {arXiv preprint arXiv:2601.07979},
year = {2026}
}
Comments
19 pages, 7 figures