Gromov-Wasserstein Graph Coarsening

2025-11-11

AI Summary

This paper addresses the challenge of preserving global structural properties during graph coarsening. We propose a novel coarsening framework grounded in Gromov–Wasserstein (GW) geometry, which explicitly models structural distortion induced by node-pair merging as the GW distance between local neighborhoods. Building on this formulation, we design two efficient algorithms: Greedy Pair Coarsening (GPC), which optimizes merges greedily, and k-means-enhanced GPC, which further enforces cluster-level consistency. We theoretically derive an error bound guaranteeing approximation to the optimal coarse graph. Extensive experiments on six large-scale graph datasets and downstream clustering tasks demonstrate that our method consistently outperforms state-of-the-art graph coarsening approaches in compression ratio, structural fidelity, and task performance—particularly under high compression ratios, where it exhibits superior robustness.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We study the problem of graph coarsening within the Gromov-Wasserstein geometry. Specifically, we propose two algorithms that leverage a novel representation of the distortion induced by merging pairs of nodes. The first method, termed Greedy Pair Coarsening (GPC), iteratively merges pairs of nodes that locally minimize a measure of distortion until the desired size is achieved. The second method, termed $k$-means Greedy Pair Coarsening (KGPC), leverages clustering based on pairwise distortion metrics to directly merge clusters of nodes. We provide conditions guaranteeing optimal coarsening for our methods and validate their performance on six large-scale datasets and a downstream clustering task. Results show that the proposed methods outperform existing approaches on a wide range of parameters and scenarios.

Problem

• Develops graph coarsening methods using Gromov-Wasserstein geometry
• Proposes algorithms to minimize distortion when merging graph nodes
• Validates performance on large datasets and clustering tasks

Innovation

• Leveraging Gromov-Wasserstein geometry for graph coarsening
• Using pairwise node merging distortion for coarsening algorithms
• Combining k-means clustering with greedy pair merging