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Population-scale single-cell multi-omics offers unprecedented opportunities to link molecular variation to human health and disease. However, existing methods for single-cell multi-omics analysis are either cell-centric, prioritizing batch-corrected cell embeddings that neglect feature relationships, or feature-centric, imposing global feature representations that overlook inter-sample heterogeneity. To address these limitations, we present MOSAIC, a spectral framework that learns a high-resolution feature × sample joint embedding from population-scale single-cell multi-omics data. For each individual, MOSAIC constructs a sample-specific coupling matrix capturing complete intra- and cross-modality feature interactions, then projects these into a shared latent space via spectral decomposition. The joint feature × sample embedding defines each feature's connectivity profile per sample, enabling two key downstream applications. First, MOSAIC introduces Differential Connectivity (DC) analysis, which identifies features exhibiting regulatory network rewiring across conditions even when their expression or abundance remains unchanged. Applied to a CITE-seq vaccination cohort, MOSAIC revealed rewiring of proliferation programs in activated T cells, highlighting a functional shift in STAT5B despite stable expression. Second, MOSAIC enables identification of biologically meaningful sample subgroups by isolating coherent multi-modal feature modules. Applied to an HIV+ prefrontal cortex cohort, MOSAIC uncovered a novel stress-driven neuronal subtype within HIV+ samples characterized by elevated protein synthesis without chromatin accessibility changes. MOSAIC provides a general-purpose framework for systems-level phenotypic characterization, offering novel biological insights from population-scale multi-omic studies.