Topological Learning for Brain Networks

Abstract

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if brain networks are genetically heritable. The challenge here is due to the difficulty of overlaying the topologically different functional brain networks obtained from resting-state functional MRI onto the template structural brain network obtained through diffusion MRI.

31 pages, 14 figures, 4 tables, code at https://github.com/topolearn

References in corpus (10)

• Persistent homology analysis of protein structure, flexibility and folding
• Sliced Wasserstein Kernel for Persistence Diagrams
• Topology-Preserving Deep Image Segmentation
• Generalized Sliced Wasserstein Distances
• Topological Deep Learning
• KerGM: Kernelized Graph Matching
• Lattice Paths for Persistent Diagrams
• Fast Topological Clustering with Wasserstein Distance
• Representations, Metrics and Statistics For Shape Analysis of Elastic Graphs
• Topological Classification in a Wasserstein Distance Based Vector Space