A multi-scale graph frequency network for structural and functional region analysis in spatial transcriptomics

Spatial transcriptomics enables the systematic exploration of how gene expression patterns are organized within intact tissues, yet effective analysis remains difficult due to the complexity of spatial dependencies and multi-scale tissue architectures. Here, we present the Spatial Graph Frequency Network (SGFN), a deep learning framework that integrates graph signal processing, graph attention, and contrastive learning to jointly model spatial topology and molecular features. Central to SGFN is a frequency-domain enhancement module that decomposes spatial graphs into multi-scale spectral components using the Laplacian eigenbasis, complemented by adaptive wavelet denoising when the retained graph-frequency sequence length permits valid decomposition. Evaluation across diverse biological systems-including the human dorsolateral prefrontal cortex, mouse brain, human breast cancer, osmFISH, MERFISH, STARmap, mouse embryonic development, head and neck angiosarcoma, and brain metastasis-shows that SGFN achieves improved or competitive performance relative to representative baseline methods in reference-based benchmarks, and identifies biologically coherent spatial or functional regions in unlabeled datasets supported by marker-gene, spatial-autocorrelation, cell-type-colocalization, and pathway-enrichment evidence. SGFN accurately reconstructed cortical layer architecture in the human brain, delineated immune and metabolic modules in tumors, and revealed spatiotemporal trajectories during embryogenesis. By combining interpretable frequency-domain representations with data-driven learning, SGFN provides a unified computational framework for decoding tissue organization and molecular heterogeneity, advancing the understanding of developmental, physiological, and pathological spatial systems.