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. 2022 Jul 14;13:4076. doi: 10.1038/s41467-022-31739-w

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a The input ST dataset consist of an expression count matrix and spatial coordinates of spots/cells. b A spatial expression graph (SEG) is constructed as the network input, with edges characterizing the spatial neighborhood, and nodes representing cells/spots with expression profiles attached. By randomly permuting the nodes in SEG, Expression Permuted Graphs (EPG) are built as negative samples. c A two-layer GCN encodes the SEG or EPG input into low-dimensional embeddings. d The embeddings are regularized for spatial consistency. With the Spatial Regularization loss and the Discriminator loss, the encoder is iteratively trained until convergence. e The low-dimensional embedding is obtained from the trained encoder. f The output consists of the pseudo-Spatiotemporal Map (pSM), domain segmentation, and the visualization of low-dimensional embeddings.