Quadra-Brain: Quadruplet Higher-Order Topological Representation Learning for fMRI-Based Brain Disorder Diagnosis.

Accurately characterizing higher-order coordination among distributed brain regions is important for understanding brain disorders from fMRI data. Existing methods mainly rely on pairwise connectivity or low-order motifs, which may overlook disease-related alterations in collective multi-region communication and higher-dimensional topological organization. To address this limitation, we propose Quadra-Brain, a computational framework for modeling quadruplet higher-order interactions in fMRI-based brain disease diagnosis. Quadra-Brain first estimates time-resolved quadruplet co-fluctuations using the multiplication of temporal derivatives, enabling the detection of transient four-region coordination patterns. It then constructs weighted brain simplicial complexes and employs two persistent-homology-based filtration processes to extract higher-dimensional neural organizations from complementary spatiotemporal perspectives. Finally, a three-branch feature fusion architecture with mutual cross-attention integrates lower-order edge features, quadruplet interaction features, and topological invariants for disease classification and interpretation. Experiments on ADNI, TaoWu, and PPMI datasets demonstrate the effectiveness and interpretability of Quadra-Brain. The learned higher-order patterns reveal disease-specific topological alterations: Alzheimer's disease progression is associated with reduced quadruplet coordination and increased topological voids, whereas Parkinson's disease shows an opposite trend. Group-level statistical analyses further indicate that the identified regions and structures are consistent with neuroscience findings. These results suggest that quadruplet interactions provide a meaningful representation of collective brain coordination and offer complementary insights beyond conventional connectivity-based analysis. The source code is publicly available at: https://github.com/Zdy12/Quadra-Brain.