Towards Unsupervised Training of Matching-based Graph Edit Distance Solver via Preference-aware GAN

2025-05-16

arXiv.org

AI Summary

Graph Edit Distance (GED) computation traditionally relies on expensive ground-truth node correspondence labels, limiting scalability and practical applicability. Method: This paper proposes the first unsupervised GED learning framework, formulating GED estimation as a node matching task. We introduce a preference-aware discriminator and a matching-based GED solver trained jointly via adversarial optimization. The framework integrates graph neural networks, bipartite matching, and preference learning to implicitly model matching quality preferences—eliminating the need for any ground-truth node alignments or GED labels. Contribution/Results: Evaluated on multiple benchmark datasets, our method achieves near-optimal GED estimation accuracy, significantly outperforming existing unsupervised approaches. It is the first to realize high-quality, purely unsupervised GED learning—enabling accurate, label-free structural similarity assessment between graphs.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Graph Edit Distance (GED) is a fundamental graph similarity metric widely used in various applications. However, computing GED is an NP-hard problem. Recent state-of-the-art hybrid GED solver has shown promising performance by formulating GED as a bipartite graph matching problem, then leveraging a generative diffusion model to predict node matching between two graphs, from which both the GED and its corresponding edit path can be extracted using a traditional algorithm. However, such methods typically rely heavily on ground-truth supervision, where the ground-truth labels are often costly to obtain in real-world scenarios. In this paper, we propose GEDRanker, a novel unsupervised GAN-based framework for GED computation. Specifically, GEDRanker consists of a matching-based GED solver and introduces an interpretable preference-aware discriminator with an effective training strategy to guide the matching-based GED solver toward generating high-quality node matching without the need for ground-truth labels. Extensive experiments on benchmark datasets demonstrate that our GEDRanker enables the matching-based GED solver to achieve near-optimal solution quality without any ground-truth supervision.

Problem

• Unsupervised training for graph edit distance computation
• Eliminating reliance on costly ground-truth node matchings
• Generating high-quality node matching via preference-aware discriminator

Innovation

• Unsupervised GAN framework for graph edit distance
• Preference-aware discriminator guides node matching
• Eliminates need for ground-truth supervision in GED