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.

翻译：在空间盲源分离中，观测到的多元随机场被视为潜在空间依赖随机场的混合。目标是通过估计解混变换来恢复潜在随机场。目前，空间盲源分离算法仅能估计线性解混变换。针对空间数据的非线性盲源分离方法较为稀缺。本文将一个可辨识的变分自编码器扩展到空间依赖数据，使其能够估计非线性解混变换，并通过仿真展示了其在平稳与非平稳空间数据上的性能。此外，我们引入了缩放平均绝对沙普利加性解释，用于通过非线性混合变换解释潜在成分。将该空间可辨识变分自编码器应用于地球化学数据集以发现潜在随机场，并利用缩放平均绝对沙普利加性解释对其进行了分析。