  In spatial blind source separation the observed multivariate random fields
are assumed to be mixtures of latent spatially dependent random fields. The
objective is to recover latent random fields by estimating the unmixing
transformation. Currently, the algorithms for spatial blind source separation
can only estimate linear unmixing transformations. Nonlinear blind source
separation methods for spatial data are scarce. In this paper we extend an
identifiable variational autoencoder that can estimate nonlinear unmixing
transformations to spatially dependent data and demonstrate its performance for
both stationary and nonstationary spatial data using simulations. In addition,
we introduce scaled mean absolute Shapley additive explanations for
interpreting the latent components through nonlinear mixing transformation. The
spatial identifiable variational autoencoder is applied to a geochemical
dataset to find the latent random fields, which are then interpreted by using
the scaled mean absolute Shapley additive explanations. Finally, we illustrate
how the proposed method can be used as a pre-processing method when making
multivariate predictions.
