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

TL;DR

This paper introduces GEDRanker, an unsupervised GAN framework that improves graph edit distance computation by guiding a matching-based solver with preference signals, eliminating the need for costly ground-truth data.

Contribution

It presents a novel unsupervised, preference-aware GAN approach for graph edit distance calculation, reducing reliance on ground-truth supervision and enhancing solution quality.

Findings

Achieves near-optimal GED without ground-truth supervision

Outperforms existing supervised methods on benchmark datasets

Demonstrates effectiveness of preference signals in guiding graph matching

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 node matchings 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. By leveraging preference signals over different node matchings derived from edit path lengths, the discriminator can guide the matching-based solver toward generating high-quality node matching without the need for ground-truth supervision. 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.