Revealing Brain and Spinal Cord Functional Networks by Block-Structured Graph Laplacian Mixture Models

The Graph Laplacian Mixture Model (GLMM) allows to infer multiple underlying graph structures from multivariate time series data. Given its effectiveness in identifying brain states from brain activity measured by functional magnetic resonance imaging (fMRI), we adapt GLMM for block-structured datasets, where data is organized into communities with strong intra-community interactions and relatively weak inter-community connections. This modification of the GLMM enables to capture the intricate structure inherent to block-structured datasets, such as fMRI data that simultaneously covers brain and cervical spinal cord, which both come with different properties. By integrating the prior knowledge on community structure into the GLMM framework, we proposed an approach that more accurately reflects the hierarchical organization and interaction patterns present in these complex networks. This enhancement offers a powerful tool for studying networked systems with distinct community structures, improving our ability to interpret patterns and dynamics in neural data with natural sub-structural organization.