SpatialHSM: A multi-scale spatial domain identification framework via frequency–state fusion and contrastive learning

Spatial transcriptomics (ST) enables spatially resolved analysis of tissue architecture and cellular heterogeneity, but high dimensionality, sparsity, and complex spatial dependencies remain challenging. We propose SpatialHSM, a multi-scale spatial domain identification framework integrating frequency-domain graph signal processing, hierarchical state-space modeling, and contrastive learning. It combines Coiflet-4 wavelet and Gaussian filters to capture multi-scale spatial patterns, fuses graph-attention propagation with node-wise HSM-SSD modulation, and employs a spatial-neighborhood contrastive objective to improve representation separability. Across diverse platforms, species, and tissues, SpatialHSM achieved competitive or superior performance, improving the adjusted Rand index (ARI) by 13.1 % on a representative human dorsolateral prefrontal cortex section, 34.0 % on STARmap, and 15.3 % on mouse sagittal brain. It also ran stably on a larger dataset containing 18,408 spatial spots and identified biologically relevant layer- and tumor-specific markers. An exploratory analysis of three pediatric PFA samples revealed preliminary age-associated tumor–immune spatial patterns requiring validation in larger cohorts. These results demonstrate the utility and generalizability of SpatialHSM for spatial domain identification and spatial omics analysis.