An expectation-maximization algorithm for the matrix normal distribution with an application in remote sensing

Dramatic increases in the size and dimensionality of many modern datasets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization (EM) algorithm for the matrix normal distribution, a distribution well-suited for naturally structured data such as spatio-temporal data. We review previously established maximum likelihood matrix normal estimates, and then consider the situation involving missing data. We apply our EM method in a simulation study exploring errors across different dimensions and proportions of missing data. We compare these errors to those from three alternative methods and show that our proposed EM method outperforms them in all scenarios. Finally, we implement the proposed EM method in a novel way on a satellite image dataset to investigate land-cover classification separability.