Graph Fourier transform for spatial omics representation and analyses of complex organs.

Spatial omics technologies are capable of deciphering detailed components of complex organs or tissue in cellular and subcellular resolution. A robust, interpretable, and unbiased representation method for spatial omics is necessary to illuminate novel investigations into biological functions, whereas a mathematical theory deficiency still exists. We present SpaGFT (Spatial Graph Fourier Transform), which provides a unique analytical feature representation of spatial omics data and elucidates molecular signatures linked to critical biological processes within tissues and cells. It outperformed existing tools in spatially variable gene prediction and gene expression imputation across human/mouse Visium data. Integrating SpaGFT representation into existing machine learning frameworks can enhance up to 40% accuracy of spatial domain identification, cell type annotation, cell-to-spot alignment, and subcellular hallmark inference. SpaGFT identified immunological regions for B cell maturation in human lymph node Visium data, characterized secondary follicle variations from in-house human tonsil CODEX data, and detected extremely rare subcellular organelles such as Cajal body and Set1/COMPASS. This new method lays the groundwork for a new theoretical model in explainable AI, advancing our understanding of tissue organization and function.