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 IMPLEMENTATION: https://github.com/kuanglab/GraphTucker.