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arXiv · 2601.07979

Spatial Covariance Constraints for Gaussian Mixture Models

Hanzhang Lu·Keiran Malott·Venkat Suprabath Bitra·Kirsty Milligan·Sanjeena Subedi·Edana Cassol·Vinita Chauhan·Connor McNairn·Bryan Muir·Prarthana Pasricha·Sangeeta Murugkar·Rowan Thomson·Andrew Jirasek·Jeffrey L. Andrews
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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.

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Hanzhang Lu, Keiran Malott, Venkat Suprabath Bitra, Kirsty Milligan, Sanjeena Subedi, Edana Cassol, Vinita Chauhan, Connor McNairn, Bryan Muir, Prarthana Pasricha, Sangeeta Murugkar, Rowan Thomson, Andrew Jirasek, Jeffrey L. Andrews. 2026-01-12. Spatial Covariance Constraints for Gaussian Mixture Models. https://arxiv.org/abs/2601.07979

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