Dynamic Brain Network Modeling Based on Nonlinear Low-Rank Manifold Regularization

Functional brain network modeling plays a crucial role in uncovering cognitive mechanisms and identifying abnormalities associated with brain disorders. However, traditional approaches—such as Pearson correlation and mutual information—typically assume that interregional relationships are static and linear, limiting their ability to capture dynamic interactions and nonlinear features. To address this limitation, we propose a nonlinear dynamic low-rank representation method. This approach constructs interregional similarity weights using physiological state matrices and Frobenius distance, while incorporating neighborhood information to generate a row-stochastic transition matrix, thereby enhancing the robustness of local connections. Additionally, a dynamic interaction effect matrix is constructed based on the stationary distribution eigenvectors, enabling the identification of both direct and indirect information transmission processes between brain regions. The method preserves the brain’s modular structure through low-rank representation and manifold regularization. Experimental results demonstrate that the proposed method not only effectively reveals dynamic information transmission pathways, cross-modular cooperative effects, and task-dependent hub reorganization patterns, but also significantly outperforms traditional static connectivity approaches. This study offers a mathematically rigorous and physiologically interpretable framework for dynamic brain network modeling and lays a theoretical foundation for the detection of dynamic abnormalities in mental disorders.