Fig. 2

Model workflow testing independencies between gene expression and spatial locations in spatial transcriptomics data. A Spatial transcriptomics technology has enabled multiplexed profiling of cellular transcriptomes and spatial locations. B In spatial transcriptomics data, the transcriptome information is represented by a matrix with genes as rows and spatial locations as columns. Distances between the spatial locations are obtained based on their coordinates. C Covariance matrices of gene expressions and spatial coordinates are calculated based on the gene expression and spatial coordinates, respectively. D Test of significance on whether the gene expressions are independent of the spatial coordinates using the covariance matrices. E Model spatial transcriptomics data using graphs, where each node corresponds to a spatial location, and two nodes are connected if they have proximate locations or similar expression profiles. Graph convolutional networks can aggregate features from each spatial location’s neighbors through convolutional layers and utilize the learned representation to perform node classification, community detection, and link prediction. Extended applications include spatial decomposition, localized expression pattern identification, and cell-cell interaction inference