Multi-site, multi-pollutant atmospheric data analysis using Riemannian geometry

We demonstrate the benefits of using Riemannian geometry in the analysis of multi-site, multi-pollutant atmospheric monitoring data. Our approach uses covariance matrices to encode spatio-temporal variability and correlations of multiple pollutants at different sites and times. A key property of covariance matrices is that they lie on a Riemannian manifold and one can exploit this property to facilitate dimensionality reduction, outlier detection, and spatial interpolation. Specifically, the transformation of data using Reimannian geometry provides a better data surface for interpolation and assessment of outliers compared to traditional data analysis tools that assume Euclidean geometry. We demonstrate the utility of using Riemannian geometry by analyzing a full year of atmospheric monitoring data collected from 34 monitoring stations in Beijing, China.