Graph Edit Distance with General Costs Using Neural Set Divergence

TL;DR

This paper introduces GRAPHEDX, a neural network-based method for estimating Graph Edit Distance with general, customizable costs for edit operations, outperforming existing methods across various datasets.

Contribution

We propose a novel neural GED estimator that explicitly incorporates general edit costs and uses neural set divergence with learned alignments.

Findings

GRAPHEDX outperforms state-of-the-art methods in prediction accuracy.

The method effectively handles various edit cost configurations.

Experiments demonstrate robustness across multiple datasets.

Abstract

Graph Edit Distance (GED) measures the (dis-)similarity between two given graphs, in terms of the minimum-cost edit sequence that transforms one graph to the other. However, the exact computation of GED is NP-Hard, which has recently motivated the design of neural methods for GED estimation. However, they do not explicitly account for edit operations with different costs. In response, we propose GRAPHEDX, a neural GED estimator that can work with general costs specified for the four edit operations, viz., edge deletion, edge addition, node deletion and node addition. We first present GED as a quadratic assignment problem (QAP) that incorporates these four costs. Then, we represent each graph as a set of node and edge embeddings and use them to design a family of neural set divergence surrogates. We replace the QAP terms corresponding to each operation with their surrogates. Computing such neural set divergence require aligning nodes and edges of the two graphs. We learn these alignments using a Gumbel-Sinkhorn permutation generator, additionally ensuring that the node and edge alignments are consistent with each other. Moreover, these alignments are cognizant of both the presence and absence of edges between node-pairs. Experiments on several datasets, under a variety of edit cost settings, show that GRAPHEDX consistently outperforms state-of-the-art methods and heuristics in terms of prediction error.