[论文解读] Graph Edit Distance Computation via Graph Neural Networks.

Yunsheng Bai, Hao Ding+4 more|arXiv (Cornell University)|Aug 16, 2018

Advanced Graph Neural Networks被引用 13

一句话总结

本文提出 SimGNN，一种基于图神经网络的方法，用于高效且准确地计算图编辑距离（GED）。通过结合可学习的图级嵌入与成对节点比较机制，SimGNN 在保持真实世界数据集上低误差率的同时，相较于基线方法实现了显著的时间减少，并展现出优越的泛化能力。

ABSTRACT

Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common Subgraph (MCS), is the core operation of graph similarity search and many other applications, but very costly to compute in practice. Inspired by the recent success of neural network approaches to several graph applications, such as node or graph classification, we propose a novel neural network based approach to address this classic yet challenging graph problem, aiming to alleviate the computational burden while preserving a good performance. The proposed approach, called SimGNN, combines two strategies. First, we design a learnable embedding function that maps every graph into a vector, which provides a global summary of a graph. A novel attention mechanism is proposed to emphasize the important nodes with respect to a specific similarity metric. Second, we design a pairwise node comparison method to supplement the graph-level embeddings with fine-grained node-level information. Our model achieves better generalization on unseen graphs, and in the worst case runs in quadratic time with respect to the number of nodes in two graphs. Taking GED computation as an example, experimental results on three real graph datasets demonstrate the effectiveness and efficiency of our approach. Specifically, our model achieves smaller error rate and great time reduction compared against a series of baselines, including several approximation algorithms on GED computation, and many existing graph neural network based models. To the best of our knowledge, we are among the first to adopt neural networks to explicitly model the similarity between two graphs, and provide a new direction for future research on graph similarity computation and graph similarity search.

研究动机与目标

• 解决图相似性搜索应用中精确图编辑距离（GED）计算的高计算成本问题。
• 与现有的基于神经网络的图相似性方法相比，提升在未见图上的泛化能力。
• 通过结合全局图嵌入与细粒度节点级比较，降低运行时间复杂度，同时保持准确性。
• 提供一种新型神经网络框架，专门设计用于建模成对图相似性，填补现有图神经网络应用中的空白。

提出的方法

• 设计一种可学习的嵌入函数，将每张图映射为向量表示，以捕捉全局结构特性。
• 引入一种新颖的注意力机制，突出对相似性度量最相关的节点，从而提升嵌入质量。
• 开发一种成对节点比较机制，通过补充图级嵌入中的细粒度节点级对应信息。
• 端到端训练模型，使用可微损失函数预测 GED 值，实现有效优化。
• 结合图级与节点级特征，以提升模型的表达能力与泛化性能。
• 实现节点数量的二次方时间复杂度，使其适用于中等规模图的可扩展计算。

实验结果

研究问题

• RQ1 神经网络能否被有效训练以实现高精度与低计算成本的图编辑距离预测？
• RQ2 与现有的近似算法和 GNN 基线相比，所提出的模型在未见图上的泛化能力如何？
• RQ3 同时引入图级与节点级信息在多大程度上提升了相似性预测性能？
• RQ4 该模型能否在保持低误差率的同时，实现相对于精确 GED 计算的显著加速？

主要发现

• 在三个真实图数据集上，SimGNN 的误差率低于多种近似算法和现有 GNN 基模型。
• 该模型在未见图上表现出强大的泛化性能，表明对分布偏移具有鲁棒性。
• 与精确 GED 计算相比，运行时间显著减少，最坏情况下的时间复杂度为节点数的二次方。
• 注意力机制能有效识别关键节点，从而提升图嵌入在相似性任务中的质量。
• 图级与成对节点级特征的结合，其性能优于单独使用任一组件。
• 据作者所知，SimGNN 是首批明确使用神经网络建模成对图相似性的模型之一。