Clustered Graph Matching for Label Recovery and Graph Classification

TL;DR

This paper introduces a clustering-based graph matching method that improves label recovery and classification accuracy in vertex-aligned networks by leveraging class-specific averages, demonstrated through theory and connectome data.

Contribution

It proposes a novel clustering and matching framework that enhances label recovery and classification in network data, with theoretical guarantees and practical validation.

Findings

Clustering networks before matching improves label recovery accuracy.

Matching to class-specific averages outperforms global average matching.

Method successfully classifies and recovers labels in real connectome data.

Abstract

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.