Strongly Topology-preserving GNNs for Brain Graph Super-resolution

TL;DR

This work develops an efficient mapping from the edge space of low-resolution (LR) brain graphs to the node space of a high-resolution (HR) dual graph, which ensures that node-level computations on this dual graph correspond naturally to edge-level learning on the authors' HR brain graphs, thereby enforcing strong topological consistency within this framework.

Abstract

Brain graph super-resolution (SR) is an under-explored yet highly relevant task in network neuroscience. It circumvents the need for costly and time-consuming medical imaging data collection, preparation, and processing. Current SR methods leverage graph neural networks (GNNs) thanks to their ability to natively handle graph-structured datasets. However, most GNNs perform node feature learning, which presents two significant limitations: (1) they require computationally expensive methods to learn complex node features capable of inferring connectivity strength or edge features, which do not scale to larger graphs; and (2) computations in the node space fail to adequately capture higher-order brain topologies such as cliques and hubs. However, numerous studies have shown that brain graph topology is crucial in identifying the onset and presence of various neurodegenerative disorders like Alzheimer and Parkinson. Motivated by these challenges and applications, we propose our STP-GSR framework. It is the first graph SR architecture to perform representation learning in higher-order topological space. Specifically, using the primal-dual graph formulation from graph theory, we develop an efficient mapping from the edge space of our low-resolution (LR) brain graphs to the node space of a high-resolution (HR) dual graph. This approach ensures that node-level computations on this dual graph correspond naturally to edge-level learning on our HR brain graphs, thereby enforcing strong topological consistency within our framework. Additionally, our framework is GNN layer agnostic and can easily learn from smaller, scalable GNNs, reducing computational requirements. We comprehensively benchmark our framework across seven key topological measures and observe that it significantly outperforms the previous state-of-the-art methods and baselines.

Figures (2)

• Figure 1: Illustration of the proposed Strongly Topology-Preserving GNN framework for Brain Graph Super-Resolution (STP-GSR). A-Target Edge Initializer. We use the source graph to guide the initialization of our dual graphs. First, we pass each source graph $\mathcal{G}_s$ with adjacency matrix $\mathbf{A}_s$ and node feature matrix $\mathbf{X}^0_s$ through our GNN layer to learn rich node embeddings. Then, using matrix multiplication and min-max scaling, the node embeddings are transformed into a scalar edge feature matrix $\mathbf{X}^0_t$ for the target graph. In the next stage, these features are converted to dual node features. B-Dual Graph Learner. We use Primal2Dual conversion to map the learned edges to dual nodes, i.e., we flatten the upper triangular part of $\mathbf{X}^0_t$ to get the dual node feature matrix $\mathbf{X}'^0_t$. We then perform node feature learning using our GNN layer in the dual space. Finally, we apply Dual2Primal conversion by mapping the learned dual node features to the upper triangular part of an empty target adjacency matrix, followed by reflection along the diagonal. This gives us the symmetric $\mathbf{A}_t$, which is our predicted connectivity matrix.
• Figure 2: Performance results. We evaluate STP-GSR across 8 different metrics against two newly created baselines and IMANGraphNet. All losses are calculated w.r.t. ground truth HR graphs. We observe that STP-GSR consistently outperforms other methods on all topological metrics. However, it does struggle to perform on the mean absolute error (MAE). We suspect this to be due to the use of a very small and shallow GNN model on the edge space.