NED：一种基于编辑距离的图间节点度量
NED: An Inter-Graph Node Metric Based On Edit Distance
摘要：
节点相似性是图分析中的一个基本问题。然而，不同图中的节点（图间节点）之间的节点相似性还没有得到很多关注。图间节点相似性在基于现有图的知识学习新图（图上的迁移学习）中是重要的，并且在生物、通信和社交网络中具有应用。在本文中，我们提出了一种新的距离函数，用于测量图间节点的相似性与编辑距离，称为NED。在NED中，两个节点根据它们的局部邻域结构进行比较，这些邻域结构表示为无序的k-相邻树，而不依赖于标签或其他假设。由于无序树的树编辑距离的计算问题是NP-完全的，我们提出了一个修改的树编辑距离，称为TED*，用于比较邻居树。TED* 是一个度量距离，作为原始树编辑距离，但更重要的是，TED* 是多项式可计算的。作为一种度量距离，NED承认有效的索引，提供可解释的结果，并在许多数据分析任务上表现得比现有方法更好，包括图形去匿名化。最后，NED的效率和有效性的实证证明使用现实世界的图表。
英文摘要：
Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received a lot of attention yet. The inter-graph node similarity is important in learning a new graph based on the knowledge of an existing graph (transfer learning on graphs) and has applications in biological, communication, and social networks. In this paper, we propose a novel distance function for measuring inter-graph node similarity with edit distance, called NED. In NED, two nodes are compared according to their local neighborhood structures which are represented as unordered k-adjacent trees, without relying on labels or other assumptions. Since the computation problem of tree edit distance on unordered trees is NP-Complete, we propose a modified tree edit distance, called TED*, for comparing neighborhood trees. TED* is a metric distance, as the original tree edit distance, but more importantly, TED* is polynomially computable. As a metric distance, NED admits efficient indexing, provides interpretable results, and shows to perform better than existing approaches on a number of data analysis tasks, including graph de-anonymization. Finally, the efficiency and effectiveness of NED are empirically demonstrated using real-world graphs.
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