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arXiv 2205.034862022-05stat.MLcs.LGstat.ME

Clustered Graph Matching for Label Recovery and Graph Classification

University of Maryland（马里兰大学）；Texas A&M University（得克萨斯农工大学）；Johns Hopkins University（约翰斯·霍普金斯大学）

Zhirui Li, Jesus Arroyo, Konstantinos Pantazis, Vince Lyzinski

备注：: 22 pages, 8 figures, 5 tables

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Given a collection of vertex-aligned networks and an additional label-shuffled network, we propose procedures for leveraging the signal in the vertex-aligned collection to recover the labels of the shuffled network. We consider matching the shuffled network to averages of the networks in the vertex-aligned collection at different levels of granularity. We demonstrate both in theory and practice that if the graphs come from different network classes, then clustering the networks into classes followed by matching the new graph to cluster-averages can yield higher fidelity matching performance than matching to the global average graph. Moreover, by minimizing the graph matching objective function with respect to each cluster average, this approach simultaneously classifies and recovers the vertex labels for the shuffled graph. These theoretical developments are further reinforced via an illuminating real data experiment matching human connectomes.

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