🤖 AI Summary
This work addresses the problem of recovering the hidden vertex correspondence between two correlated graphs while jointly leveraging edge weights and node features. To this end, the authors introduce a correlated Gaussian Wigner model with node features, where both graph structure and features are coupled through an unknown permutation. The key contribution lies in the first systematic characterization of the information-theoretic limits of this alignment problem, accompanied by the development of QPAlign—an efficient algorithm grounded in quadratic programming relaxation that integrates statistical inference with optimization techniques and enjoys theoretical guarantees. Extensive experiments demonstrate that QPAlign achieves superior performance on both synthetic and real-world datasets, and theoretical analysis confirms its convergence and reliability.
📝 Abstract
This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge information, many real-world applications provide informative node features in addition to graph topology. To capture this setting, we introduce the featured correlated Gaussian Wigner model, where two graphs are coupled through an unknown vertex permutation, and the node features are correlated under the same permutation. We characterize the optimal information-theoretic thresholds for exact recovery and partial recovery of the latent mapping. On the algorithmic side, we propose QPAlign, an algorithm based on a quadratic programming relaxation, and demonstrate its strong empirical performance on both synthetic and real datasets. Moreover, we also derive theoretical guarantees for the proposed procedure, supporting its reliability and providing convergence guarantees.