Coidentification of Group-Level Hole Structures in Brain Networks via Hodge Laplacian

One of outstanding issues in brain network analysis is to extract common topological substructure shared by a group of individuals. Recently, methods to detect group-wise modular structure on graph Laplacians have been introduced. From the perspective of algebraic topology, the modules or clusters are the zeroth topology information of a topological space. Higher order topology information can be found in holes. In this study, we extend the concept of graph Laplacian to higher order Hodge Laplacian of weighted networks, and develop a group-level hole identification method via the Stiefel optimization. In experiments, we applied the proposed method to three synthetic data and Alzheimer’s disease neuroimaing initiative (ADNI) database. Experimental results showed that the coidentification of group-level hole structures helped to find the underlying topology information of brain networks that discriminate groups well.