Mixtures of spatial factor analyzers for tensor-variate data

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.