Topology-aware Graph Diffusion Model with Persistent Homology
Keywords: Graph Generation, Diffusion, Topology, Brain Network
TL;DR: We propose a diffusion-based topology-aware graph generation method that aims to closely resemble the structural characteristics of the original graph by leveraging persistent homology from topological data analysis (TDA).
Abstract: Generating realistic graphs presents challenges in estimating accurate distribution of graphs in an embedding space while preserving structural characteristics such as topology. However, existing graph generation methods primarily focus on approximating the joint distribution of graph nodes and edges, overlooking topology-wise similarity hindering accurate representation of global graph structures such as connected components and loops. To address this issue, we propose a topology-aware diffusion-based graph generation method that aims to closely resemble the structural characteristics of the original graph by leveraging persistent homology from topological data analysis (TDA). Specifically, we suggest a novel loss function, Persistence Diagram Matching (PDM) loss, which ensures the generated graphs to closely match the topology of the original graphs, enhancing their fidelity and preserving essential homological properties. Also, we introduce a novel topology-aware attention to enhance the self-attention module in the denoising network. Through comprehensive experiments, we demonstrate the effectiveness of our approach not only by exhibiting high generation performance across various metrics, but also by demonstrating a closer alignment with the distribution of topological features observed in the original graphs. In addition, application to real brain network data showcases its versatility and potential for complex and real graph application.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 6396
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