Computer Science > Information Retrieval
[Submitted on 10 Jun 2021 (v1), last revised 11 Jun 2021 (this version, v2)]
Title:GRASP: Graph Alignment through Spectral Signatures
View PDFAbstract: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.
Submission history
From: Judith Hermanns [view email][v1] Thu, 10 Jun 2021 13:19:25 UTC (994 KB)
[v2] Fri, 11 Jun 2021 08:20:01 UTC (994 KB)
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