# Spatial Covariance Constraints for Gaussian Mixture Models

arXiv: https://arxiv.org/abs/2601.07979 · HTML: https://mlsanity.com/paper/2601.07979/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 31 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 2 of 2)

- [A Mixture of Generalized Hyperbolic Distributions](https://mlsanity.com/paper/1305.1036/) (2013)
- [A Doubly-Enhanced EM Algorithm for Model-Based Tensor Clustering](https://mlsanity.com/paper/2012.10032/) (2020)

## Built on by (most cited first, 2 of 2)

- [Mixtures of spatial factor analyzers for tensor-variate data](https://mlsanity.com/paper/2607.07887/) (2026)
- [An efficient EM algorithm for both element-wise and structural missingness in matrix-variate normal mixture models](https://mlsanity.com/paper/2609.00616/) (2026)

## Abstract (arXiv)

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.