Local Difference Matrices for Spatial Blind Source Separation

Multivariate geochemical data possess many challenges for statistical modeling, such as the multivariate dependencies between the chemicals on-site and the spatial dependencies that need to be considered. Recently, spatial blind source separation (SBSS) was suggested, where it is assumed that the multivariate measurements are formed as linear combinations of unobserved random fields that are uncorrelated and fulfill second-order stationarity assumptions. In this work, we refine SBSS by suggesting a new local covariance matrix which is based on local differences. This leads to a more robust SBSS approach which can tolerate violations of the second-order stationarity assumption. We illustrate our approach by analyzing a geochemical dataset derived from the GEMAS project.