The need to identify graphs having small structural distance from a query arises in biology, chemistry, recommender systems, and social network analysis. Among several methods to measure inter graph distance, Graph Edit Distance (GED) is preferred for its comprehensibility, yet hindered by the NP-hardness of its computation. State-of-the-art GED approximations predominantly employ neural methods, which, however, (i) lack an explanatory edit path corresponding to the approximated GED; (ii) require the NP-hard generation of ground-truth GEDs for training; and (iii) necessitate separate training on each dataset. In this paper, we propose an efficient algebraic unsuper vised method, EUGENE, that approximates GED and yields edit paths corresponding to the approx imated cost, while eliminating the need for ground truth generation and data-specific training. Extensive experimental evaluation demonstrates that the aforementioned benefits of EUGENE do not come at the cost of efficacy. Specifically, EUGENE consistently ranks among the most accurate methods across all of the benchmark datasets and outperforms majority of the neural approaches.

翻译：识别与查询图具有较小结构距离的图在生物学、化学、推荐系统及社交网络分析中具有重要需求。在多种图间距离度量方法中，图编辑距离因其可理解性备受青睐，但其计算复杂度属于NP难问题。当前最先进的图编辑距离近似方法主要采用神经网络技术，然而这些方法存在以下局限：（i）缺乏与近似图编辑距离对应的可解释编辑路径；（ii）训练过程中需要生成NP难的真实图编辑距离作为标注数据；（iii）需针对每个数据集单独训练。本文提出一种高效的代数无监督方法EUGENE，该方法可近似图编辑距离并生成与近似代价对应的编辑路径，同时消除了对真实标注生成和特定数据训练的需求。大量实验评估表明，EUGENE在兼顾上述优势的同时并未牺牲有效性：在所有基准数据集中，其准确率始终位居最优方法之列，且优于多数神经网络方法。