A1 Journal article (refereed)
Nonlinear blind source separation exploiting spatial nonstationarity (2024)

Sipilä, M., Nordhausen, K., & Taskinen, S. (2024). Nonlinear blind source separation exploiting spatial nonstationarity. Information Sciences, 665, Article 120365. https://doi.org/10.1016/j.ins.2024.120365

JYU authors or editors

Publication details

All authors or editorsSipilä, Mika; Nordhausen, Klaus; Taskinen, Sara

Journal or seriesInformation Sciences



Publication year2024

Publication date28/02/2024


Article number120365


Publication countryUnited States

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessPartially open access channel

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/93820

Web address of parallel published publication (pre-print)https://arxiv.org/abs/2311.08004


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.

Keywordsspatial analysissignal processingindependent component analysis

Free keywordsindependent component analysis; multivariate spatial data; Shapley values; variational autoencoder

Contributing organizations

Ministry reportingYes

Reporting Year2024

Preliminary JUFO rating3

Last updated on 2024-13-05 at 18:25