Fig. 1: Overview of GraphST.

A GraphST takes as inputs the preprocessed spatial gene expressions and neighborhood graph constructed using spot coordinates (\(x,y\)). Latent representation \({Z}_{s}\) is first learned using our graph self-supervised contrastive learning to preserve the informative features from the gene expression profiles, spatial location information, and local context information. This is then reversed back into the original feature space to reconstruct the gene expression matrix \({H}_{s}\). B The analysis workflow for spatial batch effect correction by GraphST. The first step is to align the H&E images of two or more samples, followed by shared neighborhood graph construction, where both intra- and inter-sample neighbors are considered. This provides the possibility for feature smoothing. Finally, sample batch effects are implicitly corrected by smoothing features across samples with GraphST. C With the reconstructed spatial gene expression \({H}_{s}\) and the refined scRNA-seq feature matrix \({H}_{c}\) derived from an unsupervised auto-encoder, a cell-to-spot mapping matrix \(M\) is trained via a spatially informed contrastive learning mechanism where the similarities of positive pairs (i.e., spatially adjacent spot pairs) are maximized, and those of negative pairs (i.e., spatially nonadjacent spot pairs) are minimized. D The outputs \({H}_{s}\) and \(M\) of GraphST can be utilized for spatial clustering, multiple ST data integration, and ST and scRNA-seq data integration.