arXiv 1805.014192018-05-03cs.SIcs.DS

图的动态结构相似性

Dynamic Structural Similarity on Graphs

Eduar Castrillo, Elizabeth León, Jonatan Gómez

备注：: 8 pages, 7 figures, 1 table, Submitted for peer-review to the conference ASONAM 2018

摘要：

描述图中顶点和边的拓扑和结构性质的一种方法是使用结构相似性度量。像余弦、Jaccard和Dice这样的度量方法计算的相似性仅限于顶点的直接邻域，绕过了局部性之外的重要结构属性。其他措施，如广义边缘聚类系数，超越了局部性，但具有较高的计算复杂性，使他们在大规模的场景不切实际。在本文中，我们提出了一种新的相似性度量，确定结构的相似性，通过动态扩散和捕获信息超出了本地。这种新的相似度被建模为一个迭代函数，可以在超线性的时间和内存复杂度下通过不动点迭代来求解，因此它能够分析大规模的图。为了在社区发现任务中显示所提出的相似性的优点，我们用所提出的相似性度量代替SCAN算法中使用的局部结构相似性，提高了检测到的社区结构的质量，并且还降低了SCAN算法对参数$ε$的敏感性。

英文摘要：

One way of characterizing the topological and structural properties of vertices and edges in a graph is by using structural similarity measures. Measures like Cosine, Jaccard and Dice compute the similarities restricted to the immediate neighborhood of the vertices, bypassing important structural properties beyond the locality. Others measures, such as the generalized edge clustering coefficient, go beyond the locality but with high computational complexity, making them impractical in large-scale scenarios. In this paper we propose a novel similarity measure that determines the structural similarity by dynamically diffusing and capturing information beyond the locality. This new similarity is modeled as an iterated function that can be solved by fixed point iteration in super-linear time and memory complexity, so it is able to analyze large-scale graphs. In order to show the advantages of the proposed similarity in the community detection task, we replace the local structural similarity used in the SCAN algorithm with the proposed similarity measure, improving the quality of the detected community structure and also reducing the sensitivity to the parameter $ε$ of the SCAN algorithm.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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