From Nodes to Edges: Edge-Based Laplacians for Brain Signal Processing

TL;DR

This paper introduces an edge-centric graph signal processing method using the Hodge Laplacian to analyze brain connectivity, revealing new insights and improving task decoding accuracy over traditional node-based approaches.

Contribution

It presents a novel edge-based GSP framework for brain signals, capturing edge dynamics with the Hodge Laplacian, and demonstrates its superiority in decoding tasks.

Findings

Edge-based GSP outperforms node-based methods in decoding accuracy.

Edge signals reveal unique brain connectivity features.

The approach enhances understanding of brain functional organization.

Abstract

Traditional graph signal processing (GSP) methods applied to brain networks focus on signals defined on the nodes. Thus, they are unable to capture potentially important dynamics occurring on the edges. In this work, we adopt an edge-centric GSP approach to analyze edge signals constructed from 100 unrelated subjects of the Human Connectome Project. Specifically, we describe structural connectivity through the lens of the 1-dimensional Hodge Laplacian, processing signals defined on edges to capture co-fluctuation information between brain regions. We demonstrate that edge-based approaches achieve superior task decoding accuracy in static and dynamic scenarios compared to conventional node-based techniques, thereby unveiling unique aspects of brain functional organization. These findings underscore the promise of edge-focused GSP strategies for deepening our understanding of brain connectivity and functional dynamics.