Discriminative persistent homology of brain networks

Abstract

It is known that the brain network has small-world and scale-free topology, but the network structures drastically change depending on how to threshold a connectivity matrix. The exact threshold criterion is difficult to determine. In this paper, instead of trying to determine one fixed optimal threshold, we propose to look at the topological changes of brain network while increasing the threshold continuously. This process of continuously changing threshold level and looking at the resulting topological feature is related to the Rips filtration in persistent homology. The sequence of topological features obtained during the Rips filtration can be visualized and interpreted using barcode. As an illustration, we apply the Rips filtration to construct the FDG-PET based functional brain networks out of 24 attention deficit hyperactivity disorder (ADHD) children, 26 autism spectrum disorder (ASD) children and 11 pediatric control subjects. We visually show the topological evolution of the brain networks using the barcode and perform statistical inference on the group differences. This is the first paper that deals with the persistence homology of the brain networks.