1. Spectral Graph Matching and Regularized Quadratic Relaxations II: Erdős-Rényi Graphs and Universality.
- Author
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Fan, Zhou, Mao, Cheng, Wu, Yihong, and Xu, Jiaming
- Subjects
QUADRATIC assignment problem ,GRAPH algorithms ,QUADRATIC programming ,SPARSE matrices ,WEIGHTED graphs ,RANDOM matrices ,STATISTICAL correlation - Abstract
We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery guarantees established in a companion paper for Gaussian weights, in this work, we prove the universality of these guarantees for a general correlated Wigner model. In particular, for two Erdős-Rényi graphs with edge correlation coefficient 1 - σ 2 and average degree at least polylog (n) , we show that GRAMPA exactly recovers the latent vertex correspondence with high probability when σ ≲ 1 / polylog (n) . Moreover, we establish a similar guarantee for a variant of GRAMPA, corresponding to a tighter quadratic programming relaxation of the quadratic assignment problem. Our analysis exploits a resolvent representation of the GRAMPA similarity matrix and local laws for the resolvents of sparse Wigner matrices. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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