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

Spatial omics technologies decipher functional components of complex organs at cellular and subcellular resolutions. We introduce Spatial Graph Fourier Transform (SpaGFT) and apply graph signal processing to a wide range of spatial omics profiling platforms to generate their interpretable representations. This representation supports spatially variable gene identification and improves gene expression imputation, outperforming existing tools in analyzing human and mouse spatial transcriptomics data. SpaGFT can identify immunological regions for B cell maturation in human lymph nodes Visium data and characterize variations in secondary follicles using in-house human tonsil CODEX data. Furthermore, it can be integrated seamlessly into other machine learning frameworks, enhancing accuracy in spatial domain identification, cell type annotation, and subcellular feature inference by up to 40%. Notably, SpaGFT detects rare subcellular organelles, such as Cajal bodies and Set1/COMPASS complexes, in high-resolution spatial proteomics data. This approach provides an explainable graph representation method for exploring tissue biology and function.