Spatial Covariance Constraints for Gaussian Mixture Models

TL;DR

This paper introduces a spatial covariance constraint for Gaussian mixture models that reduces the number of parameters needed, enabling efficient clustering and spatial pattern inference in high-dimensional spatial data.

Contribution

It proposes a novel spatial covariance constraint requiring only four parameters per component, independent of data dimensionality, and combines EM with GLS for parameter estimation.

Findings

Effective clustering of multi-way spatial data demonstrated.

Reduced parameter complexity compared to traditional models.

Successful application to Raman spectroscopy data.

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.