Orthogonal Sparse Subgraph Alignment for Structure-Function Coupling in Brain Networks

Characterizing the relationship between brain anatomical wiring and functional coordination remains a fundamental challenge in computational neuroscience. This difficulty primarily arises because structure-function coupling in the human brain is spatially heterogeneous, often localized to subnetworks, and inherently difficult to align across disparate representational modalities. To address this methodological gap, we introduce $\textbf{O}$rthogonal $\textbf{S}$parse $\textbf{S}$ubgraph $\textbf{A}$lignment ($\textbf{Ossa}$), a principled and interpretable framework designed to identify compact structural cliques that exhibit maximal concordance with functional connectivity (FC) across subjects. Within each FC-derived community, $\textbf{Ossa}$ optimizes an alignment objective over an orthogonal transformation, which absorbs coordinate mismatch between the two connectivity modalities, and a sparse node-selection vector, which identifies the induced structural connectivity (SC) subgraph. Furthermore, we establish theoretical properties for the $\textbf{Ossa}$ estimator, demonstrating its statistical consistency in recovering the true underlying SC clique within each functional community. Extensive empirical evaluations on simulated data, alongside analyses of the Adolescent Brain Cognitive Development (ABCD) baseline and longitudinal cohorts, demonstrate that $\textbf{Ossa}$ successfully recovers aligned structural cliques under latent cross-modal rotations. Ultimately, the proposed methodology significantly improves out-of-sample SC-FC alignment over size-matched baselines and robustly identifies stable, single-core topological structures within human brain networks.