# Mixtures of spatial factor analyzers for tensor-variate data

arXiv: https://arxiv.org/abs/2607.07887 · HTML: https://mlsanity.com/paper/2607.07887/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [A Mixture of Generalized Hyperbolic Distributions](https://mlsanity.com/paper/1305.1036/) (2013)
- [Finite mixtures of matrix-variate Poisson-log normal distributions for three-way count data](https://mlsanity.com/paper/1807.08380/) (2018)
- [A Mixture of Matrix Variate Bilinear Factor Analyzers](https://mlsanity.com/paper/1712.08664/) (2017)
- [Mixtures of Contaminated Matrix Variate Normal Distributions](https://mlsanity.com/paper/2005.03861/) (2020)
- [Spatial Covariance Constraints for Gaussian Mixture Models](https://mlsanity.com/paper/2601.07979/) (2026)

## Built on by (most cited first, 1 of 1)

- [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)

A mixture of spatial factor analyzers (MSFA) is introduced to address the challenges of clustering high-dimensional spatial data. The proposed framework utilizes the given coordinate system to implement a flexible, spline-based spatial decay covariance structure. In this approach, the number of covariance parameters increases linearly with the number of spatial locations, rather than increasing quadratically. To model non-spatial dependence, matrix variate factor analyzers are employed for further dimensionality reduction. Parameter estimation is conducted via a variant of the expectation-maximization algorithm combined with a generalized least squares estimator. The proposed models are explored in the context of tensor-variate data analysis, where simulation studies and three applications---Raman spectroscopy, SpecTex hyperspectral textures, and the Salinas hyperspectral scene---illustrate their ability to recover and distinguish spatial dependence patterns. The R implementation is available on CRAN: https://CRAN.R-project.org/package=SpatMix.