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Hierarchical Graph Matching Network for Graph Similarity Computation
arXiv - CS - Databases Pub Date : 2020-06-30 , DOI: arxiv-2006.16551
Haibo Xiu, Xiao Yan, Xiaoqiang Wang, James Cheng, Lei Cao

Graph edit distance / similarity is widely used in many tasks, such as graph similarity search, binary function analysis, and graph clustering. However, computing the exact graph edit distance (GED) or maximum common subgraph (MCS) between two graphs is known to be NP-hard. In this paper, we propose the hierarchical graph matching network (HGMN), which learns to compute graph similarity from data. HGMN is motivated by the observation that two similar graphs should also be similar when they are compressed into more compact graphs. HGMN utilizes multiple stages of hierarchical clustering to organize a graph into successively more compact graphs. At each stage, the earth mover distance (EMD) is adopted to obtain a one-to-one mapping between the nodes in two graphs (on which graph similarity is to be computed), and a correlation matrix is also derived from the embeddings of the nodes in the two graphs. The correlation matrices from all stages are used as input for a convolutional neural network (CNN), which is trained to predict graph similarity by minimizing the mean squared error (MSE). Experimental evaluation on 4 datasets in different domains and 4 performance metrics shows that HGMN consistently outperforms existing baselines in the accuracy of graph similarity approximation.

中文翻译:

用于图相似度计算的分层图匹配网络

图编辑距离/相似度被广泛应用于许多任务,例如图相似度搜索、二元函数分析和图聚类。然而,计算两个图之间的精确图编辑距离 (GED) 或最大公共子图 (MCS) 是已知的 NP-hard。在本文中,我们提出了分层图匹配网络(HGMN),它学习从数据中计算图的相似性。HGMN 的动机是观察到两个相似的图在压缩成更紧凑的图时也应该相似。HGMN 利用层次聚类的多个阶段将图组织成连续更紧凑的图。在每个阶段,采用推土机距离(EMD)获得两个图(要计算图相似度)中节点之间的一对一映射,并且相关矩阵也来自两个图中节点的嵌入。来自所有阶段的相关矩阵用作卷积神经网络 (CNN) 的输入,该网络经过训练以通过最小化均方误差 (MSE) 来预测图的相似性。对不同领域的 4 个数据集和 4 个性能指标的实验评估表明,HGMN 在图相似性近似的准确性方面始终优于现有基线。
更新日期:2020-07-01
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