BrainRiem: Riemannian Prototype Learning for Source-Free Cross-Site Brain Network Diagnosis

Graph-based learning on functional magnetic resonance imaging (fMRI) has shown strong potential for brain network analysis. However, existing methods degrade under cross-site out-of-distribution (OOD) settings because site-conditioned confounders induce non-pathological shortcuts, while functional connectivity constructed by temporal averaging obscures transient neurodynamics, limiting generalization to unseen sites. In this paper, we propose Cross-site OOD Robust brain nEtwork (CORE), a unified framework for brain network learning across unseen sites. CORE first performs site-aware confounder decoupling to mitigate site-conditioned bias and extract a cross-site population scaffold of reproducible diagnostic connectivity edges. It then profiles transient pathway dynamics over this scaffold using lightweight temporal descriptors and organizes scaffold edges into a line graph for transferable pathway-level modeling. Finally, CORE introduces a prior-guided subject-adaptive gating mechanism that leverages scaffold-derived population priors while preserving subject-specific connectivity variability. Extensive experiments under leave-one-site-out evaluation on real-world datasets (ABIDE, REST-meta-MDD, SRPBS, and ABCD) show that CORE consistently outperforms state-of-the-art baselines, with up to 6.7% relative gain. Furthermore, CORE remains robust to atlas variations, maintaining performance gains across different brain parcellation schemes.

Cross-site identification of major depressive disorder (MDD) from resting-state functional magnetic resonance imaging (rs-fMRI) is hindered by inter-site distribution shifts and heterogeneous functional connectivity (FC) views. These views capture complementary neural relationships but exhibit distinct site biases and graph topologies, complicating alignment without sacrificing disease-relevant information or cross-view consistency. Existing studies largely treat multi-view connectome learning and cross-site adaptation separately. To the best of our knowledge, few studies have jointly modeled multiple FC views under multi-source unsupervised domain adaptation for cross-site rs-fMRI-based MDD classification. We construct Pearson correlation, sparse representation, and Granger causality graphs, each encoded by a view-specific graph attention network. Dual-stream adaptive fusion explicitly integrates pairwise cross-view interactions, followed by lightweight hyperbolic residual encoding for curvature-aware representation refinement. Class-wise Cauchy--Schwarz alignment reduces inter-source and source-target discrepancies, complemented by adversarial learning, information maximization, and confidence-aware pseudo-labeling. Across seven unlabeled target domains, our framework achieves 73.60% mean accuracy and 71.90% AUC, demonstrating effective generalization under heterogeneous acquisition conditions. These results highlight the effectiveness of unified heterogeneous-view modeling, curvature-aware refinement, and multi-source domain adaptation for cross-site MDD identification.The source code is at https://github.com/OPUS-Lightphenexx/MM-HyperGDA

Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form operations or depend on arbitrary region ordering, limiting scalability. We introduce a scalable geometric framework with two components: (i) the Off-log metric, a smooth transformation mapping correlation matrices to symmetric zero-diagonal matrices. This enables closed-form expressions for distances, Frechet means, and linear models, allowing standard statistical modeling without complex manifold optimization. (ii) Grassmannian subspace discrimination, which compares subjects via principal-angle distances between eigenvector subspaces, resolving inherent sign and basis ambiguities. Both components integrate into standard machine-learning workflows for inference, regression, and classification. Validated across two clinical cohorts (Parkinson's and psychosis) and three ageing fMRI datasets, the Off-log metric increased sensitivity in permutation tests and matched or exceeded Riemannian and Euclidean baselines in classification. Brain-age prediction performance was comparable, with Riemannian metrics excelling in two of three cohorts. The Grassmannian method consistently outperformed Euclidean baselines, highlighting disease-relevant networks. Overall, geometry-aware representations improve sensitivity and predictive performance while remaining straightforward to deploy at scale.