Topological Cycle Graph Attention Network for Brain Functional Connectivity

TL;DR

This work tackles the challenge of distinguishing the brain's functional backbone from redundant cycle connections in brain functional connectivity graphs derived from fMRI. It introduces CycGAT, a cycle-aware graph attention network that uses a cycle incidence matrix $T$, cycle adjacency $A_E$, and edge positional encodings in cycles $P_E$ to filter edge signals through a cycle graph convolution with attention. On the large ABCD rs-fMRI dataset, CycGAT outperforms several state-of-the-art GNNs in classifying high vs low general intelligence and reveals a sparser, more focused functional backbone, validated by ablation studies of edge positional encodings. The approach provides a topological framework for analyzing neural circuits, with potential implications for cognitive neuroscience and clinical prediction, and suggests avenues for future validation and integration with structural connectivity.

Abstract

This study, we introduce a novel Topological Cycle Graph Attention Network (CycGAT), designed to delineate a functional backbone within brain functional graph--key pathways essential for signal transmissio--from non-essential, redundant connections that form cycles around this core structure. We first introduce a cycle incidence matrix that establishes an independent cycle basis within a graph, mapping its relationship with edges. We propose a cycle graph convolution that leverages a cycle adjacency matrix, derived from the cycle incidence matrix, to specifically filter edge signals in a domain of cycles. Additionally, we strengthen the representation power of the cycle graph convolution by adding an attention mechanism, which is further augmented by the introduction of edge positional encodings in cycles, to enhance the topological awareness of CycGAT. We demonstrate CycGAT's localization through simulation and its efficacy on an ABCD study's fMRI data (n=8765), comparing it with baseline models. CycGAT outperforms these models, identifying a functional backbone with significantly fewer cycles, crucial for understanding neural circuits related to general intelligence. Our code will be released once accepted.

Figures (4)

• Figure 1: CycGAT framework overview. (a) The input graph displays nodes (circles), edges (squares), and edge signals (rectangles), with edge decomposition into a maximum-spanning tree, $B(\mathcal{G})$, and the set of additional edges, $D(\mathcal{G})$. (b) Detailing the computation of the cycle incidence matrix, iteratively applied to each edge in $D(\mathcal{G})$. (c) Depiction of cycle graph convolutional layers, with blue arrows indicating signal propagation within a single cycle and orange arrows demonstrating inter-cycle signal propagation via shared edges.
• Figure 2: Examples of the edge positional encodings in cycles (EPEC) representing the $k$-th order of eigenfunction. The frequencies $\lambda = [0.0148, 0.0296, 0.0581, 0.0799, 0.0977]$, corresponding to panels (a-e), illustrate the EPEC's ability to encode different spatial frequencies. Lower frequencies highlight global and gradual variations within the graph (e.g., top-down orientations), whereas higher frequencies reveal increasingly intricate and localized cycle patterns.
• Figure 3: CycGAT's spatial localization with four convolutional layers. (a) depicts a pulse signal at a single edge. (b-c) illustrate the signal's propagation within a cycle. (d-e) demonstrate inter-cycle signal propagation through shared edges.
• Figure 4: Panel (a) and panel (c) show the saliency maps from CycGAT and HL-HGCNN, respectively. Panel (b) shows the brain functional connectivity. The box plot in panel (d) illustrates the number of cycles in FC and saliency maps.