# Nonlinear blind source separation exploiting spatial nonstationarity

arXiv: https://arxiv.org/abs/2311.08004 · HTML: https://mlsanity.com/paper/2311.08004/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Identifiable Autoregressive Variational Autoencoders for Nonlinear and Nonstationary Spatio-Temporal Blind Source Separation](https://mlsanity.com/paper/2509.11962/) (2025)

## Abstract (arXiv)

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.