Spatial Covariance Constraints for Gaussian Mixture Models

• URL: http://arxiv.org/abs/2601.07979v1
• Date: Mon, 12 Jan 2026 20:21:22 GMT
• Title: Spatial Covariance Constraints for Gaussian Mixture Models
• Authors: 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,
• Abstract summary: This study introduces a spatial covariance constraint for Gaussian mixture models that requires only four free parameters for each component, independent of dimensionality.<n>Using a coordinate system, the spatially constrained Gaussian mixture model enables clustering of multi-way spatial data and inference of spatial patterns.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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