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.

翻译：给定一组顶点对齐网络和一个额外标签混乱的网络，我们提出了利用顶点对齐网络集合中的信号来恢复混乱网络标签的方法。我们考虑在不同粒度级别将混乱网络与顶点对齐网络集合中的平均网络进行匹配。我们从理论和实践两方面证明，如果图来自不同的网络类别，则先对网络进行聚类，再将新图与聚类平均图进行匹配，相比于匹配全局平均图能获得更高的匹配保真度。此外，通过最小化相对于每个聚类平均值的图匹配目标函数，该方法能够同时实现混乱图的分类与顶点标签恢复。通过一项揭示性的人脑连接组匹配实际数据实验，进一步验证了这些理论发展。