Blind Source Separation for Spatial Compositional Data

In regional geochemistry rock, sediment, soil, plant or water samples, collected in a certain region, are analyzed for concentrations of chemical elements. The observations are thus usually high dimensional, spatially dependent and of compositional nature. In this paper, a novel blind source separation approach for spatially dependent data is suggested. For the analysis, it is assumed that the multivariate observations are linear combinations or mixtures of latent components and that the spatial processes for these latent components are second order stationary and uncorrelated. In the present approach, the latent components are then recovered by simultaneously diagonalizing the covariance matrix and a local covariance (correlation) matrix. This method can be easily applied also in the context of compositional data after appropriate data transformations. The components obtained in this way are uncorrelated and easily interpretable, and can be used for dimension reduction and for visual presentation of different features of the data. To demonstrate the usefulness of the new method, the KOLA data are reanalyzed using the new procedure and the results are compared to the results coming from marginal principal component analysis and independent component analysis that ignore spatial dependence.