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Abstract  Spatial transcripome (ST) profiling can reveal cells’ structural organizations and functional roles in tissues. However, deciphering the spatial context of gene expressions in ST data is a challenge—the high-order structure hiding in whole transcriptome space over 2D/3D spatial coordinates requires modeling and detection of interpretable high-order elements and components for further functional analysis and interpretation. This paper presents a new method GraphTucker—graph-regularized Tucker tensor decomposition for learning high-order factorization in ST data. GraphTucker is based on a nonnegative Tucker decomposition algorithm regularized by a high-order graph that captures spatial relation among spots and functional relation among genes. In the experiments on several Visium and Stereo-seq datasets, the novelty and advantage of modeling multiway multilinear relationships among the components in Tucker decomposition are demonstrated as opposed to the Canonical Polyadic Decomposition and conventional matrix factorization models by evaluation of detecting spatial components of gene modules, clustering spatial coefficients for tissue segmentation and imputing complete spatial transcriptomes. The results of visualization show strong evidence that GraphTucker detect more interpretable spatial components in the context of the spatial domains in the tissues. Availability and implementationhttps://github.com/kuanglab/GraphTucker. 

Abstract Spatially-resolved RNA profiling has now been widely used to understand cells’ structural organizations and functional roles in tissues, yet it is challenging to reconstruct the whole spatial transcriptomes due to various inherent technical limitations in tissue section preparation and RNA capture and fixation in the application of the spatial RNA profiling technologies. Here, we introduce a graph-guided neural tensor decomposition (GNTD) model for reconstructing whole spatial transcriptomes in tissues. GNTD employs a hierarchical tensor structure and formulation to explicitly model the high-order spatial gene expression data with a hierarchical nonlinear decomposition in a three-layer neural network, enhanced by spatial relations among the capture spots and gene functional relations for accurate reconstruction from highly sparse spatial profiling data. Extensive experiments on 22 Visium spatial transcriptomics datasets and 3 high-resolution Stereo-seq datasets as well as simulation data demonstrate that GNTD consistently improves the imputation accuracy in cross-validations driven by nonlinear tensor decomposition and incorporation of spatial and functional information, and confirm that the imputed spatial transcriptomes provide a more complete gene expression landscape for downstream analyses of cell/spot clustering for tissue segmentation, and spatial gene expression clustering and visualizations.