Spatial Blind Source Separation in the Presence of a Drift

TL;DR

This paper introduces an adapted Spatial Blind Source Separation method that accounts for non-stationarity in spatial data, demonstrated through synthetic and real data applications.

Contribution

The paper formalizes an adaptation of SBSS using difference-based scatter matrices to handle non-stationary spatial data.

Findings

The adapted SBSS method effectively captures spatial dependencies in non-stationary data.

Synthetic data experiments validate the method's ability to recover latent sources.

Real data analysis demonstrates practical applicability of the proposed approach.

Abstract

Multivariate measurements taken at different spatial locations occur frequently in practice. Proper analysis of such data needs to consider not only dependencies on-sight but also dependencies in and in-between variables as a function of spatial separation. Spatial Blind Source Separation (SBSS) is a recently developed unsupervised statistical tool that deals with such data by assuming that the observable data is formed by a linear latent variable model. In SBSS the latent variable is assumed to be constituted by weakly stationary random fields which are uncorrelated. Such a model is appealing as further analysis can be carried out on the marginal distributions of the latent variables, interpretations are straightforward as the model is assumed to be linear, and not all components of the latent field might be of interest which acts as a form of dimension reduction. The weakly stationarity assumption of SBSS implies that the mean of the data is constant for all sample locations, which might be too restricting in practical applications. Therefore, an adaptation of SBSS that uses scatter matrices based on differences was recently suggested in the literature. In our contribution we formalize these ideas, suggest an adapted SBSS method and show its usefulness on synthetic and real data.