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.

翻译：在空间盲源分离中，观测到的多元随机场被假定为潜在空间相关随机场的混合。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十分稀缺。本文扩展了一种可识别的变分自编码器，使其能够估计空间相关数据的非线性解混变换，并通过仿真实验展示了该方法在平稳和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法解释，用于通过非线性混合变换解释潜在成分。我们将空间可识别变分自编码器应用于地球化学数据集以发现潜在随机场，随后利用缩放平均绝对沙普利加法解释对其进行解释。最后，我们展示了该方法如何在多元预测中作为预处理步骤使用。