A Novel Spatio-temporal Hub Identification in Brain Networks by Learning Dynamic Graph Embedding on Grassmannian Manifolds.

Mounting evidence has revealed that functional brain networks are intrinsically dynamic, undergoing changes over time, even in the rest-state environment. Notably, recent studies have highlighted the existence of a small number of critical brain regions within each functional brain network that exhibit a flexible role in adapting the geometric pattern of brain connectivity over time, referred to as "temporal hub" regions. Therefore, the identification of these temporal hubs becomes pivotal for comprehending the mechanisms that underlie the dynamic evolution of brain connectivity. However, existing spatio-temporal hub identification methods rely on static network-based approaches, wherein each temporal hub region is independently inferred from individual time-segmented networks without considering their temporal consistency and consequently fails to align the evolution of hubs with the dynamic changes in brain states. To address this limitation, we propose a novel spatio-temporal hub identification method that fully leverages dynamic graph embedding to distinguish temporal hubs from peripheral nodes, in which dynamic graph embeddings are learned from both spatial and temporal dimensions. Specifically, to preserve the temporal consistency of evolving networks, we model the dynamic graph embedding as a physical model of time, where the network-to-network transition is mathematically expressed as a total variation of dynamic graph embedding with respect to time. Furthermore, a Grassmannian manifold optimization scheme is introduced to enhance graph embedding learning and capture the time-varying topology of brain networks. Experimental results on both synthetic and real fMRI data demonstrate superior temporal consistency in hub identification, surpassing conventional approaches.