Weighted Functional Brain Network Modeling via Network Filtration

In traditional brain network modeling, an weighted brain network is often thresholded at a prespecified level to produce a binary graph for visualization and quantification. However, if we threshold the brain network and obtain only the strongly connected edges, we may lose additional information. Motivated by the persistent homology and Rips filtration, we propose a new multiscale brain network modeling framework called the network filtration, which represents the weighted network into the finite number of nested binary networks over every possible threshold. In the network filtration framework, we look at the changes of topological invariants over different thresholds. Particularly, we are interested in the changes of connected structures in the brain network, which can be represented in four different but equivalent ways: barcode, single linkage dendrogram (SLD), single linkage matrix (SLM) and minimum spanning tree (MST). Numerical experiments show that the proposed method can discriminate the local and global differences of the brain networks of 24 attention deficit hyperactivity disorder (ADHD), 26 autism spectrum disorder (ASD) and 11 pediatric control (PedCon) children obtained through the FDG-PET data.