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GRASP: Graph Alignment through Spectral Signatures
arXiv - CS - Information Retrieval Pub Date : 2021-06-10 , DOI: arxiv-2106.05729
Judith Hermanns, Anton Tsitsulin, Marina Munkhoeva, Alex Bronstein, Davide Mottin, Panagiotis Karras

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph.In this paper, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics,and then exploits this correspondence to align nodes. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that GRASP outperforms state-of-the-art methods for graph alignment across noise levels and graph types.

中文翻译:

GRASP:通过光谱特征图对齐

匹配两个图的节点的最佳方法是什么?这个图对齐问题概括了图同构,并出现在从社交网络分析到生物信息学的应用中。一些解决方案假设已知匹配或节点或边属性的辅助信息可用,或利用任意图形特征。这种方法在问题的纯形式中表现不佳,其中只给出了图结构。其他建议将问题转化为对齐节点嵌入之一,但是,通过这样做,仅提供图的单尺度视图。在本文中,我们将功能图的形状分析概念从连续情况转移到离散情况,并将图对齐问题视为在图上找到函数之间的映射问题的特例。我们提出 GRASP,一种方法,首先建立从拉普拉斯矩阵特征向量导出的函数之间的对应关系,捕获多尺度结构特征,然后利用这种对应关系来对齐节点。我们的实验研究具有比以往研究中使用的任何噪声水平都高的噪声水平,表明 GRASP 在跨噪声水平和图形类型的图形对齐方面优于最先进的方法。
更新日期:2021-06-11
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