› Research : IMAGe :: Geometric Anisotropy

›› Exploring the Latent Space of Geometric Anisotropy for Climate Datasets

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from locally varying geometric anisotropy. A Gaussian process regression using a non-stationary covariance function has shown promise for this task, as this covariance function adapts to the variable geometric anisotropy of the underlying distribution. In this work, we explore the latent space of geometric anisotropy for the non-stationary covariance function to address the aforementioned geospatial issues. Additionally, we propose a model that uses intrinsic statistics of the symmetric positive definite matrices to represent the latent space of geometric anisotropy, and, thereby, model the non-stationary covariance function. Experiments on a synthetic and real dataset of relative sea level changes across the world demonstrate improvements in the error metrics for the regression estimates using our newly proposed approach.