Clustered Graph Matching for Label Recovery and Graph Classification
This work addresses label recovery and graph classification for network data, such as in neuroscience, but it appears incremental as it builds on existing graph matching methods by incorporating clustering.
The paper tackles the problem of recovering vertex labels in a shuffled network by leveraging a collection of aligned networks, showing that clustering networks into classes and matching to cluster averages improves matching fidelity over using a global average. The approach simultaneously classifies and recovers labels, with theoretical and practical validation on human connectome data.
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.