Spatial Covariance Constraints for Gaussian Mixture Models
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arXiv
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| Autores principales: | , , , , , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908761295159296 |
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| author | Lu, Hanzhang Malott, Keiran Bitra, Venkat Suprabath Milligan, Kirsty Subedi, Sanjeena Cassol, Edana Chauhan, Vinita McNairn, Connor Muir, Bryan Pasricha, Prarthana Murugkar, Sangeeta Thomson, Rowan Jirasek, Andrew Andrews, Jeffrey L. |
| author_facet | Lu, Hanzhang Malott, Keiran Bitra, Venkat Suprabath Milligan, Kirsty Subedi, Sanjeena Cassol, Edana Chauhan, Vinita McNairn, Connor Muir, Bryan Pasricha, Prarthana Murugkar, Sangeeta Thomson, Rowan Jirasek, Andrew Andrews, Jeffrey L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07979 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spatial Covariance Constraints for Gaussian Mixture Models Lu, Hanzhang Malott, Keiran Bitra, Venkat Suprabath Milligan, Kirsty Subedi, Sanjeena Cassol, Edana Chauhan, Vinita McNairn, Connor Muir, Bryan Pasricha, Prarthana Murugkar, Sangeeta Thomson, Rowan Jirasek, Andrew Andrews, Jeffrey L. Methodology Machine Learning 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. |
| title | Spatial Covariance Constraints for Gaussian Mixture Models |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2601.07979 |