Robustness of Community Detection to Random Geometric Perturbations
This provides theoretical guarantees for community detection algorithms in noisy network data, though it appears incremental as it extends existing spectral methods to a specific perturbation model.
The paper tackles the problem of community detection in stochastic block models with random geometric perturbations, proving that spectral methods remain robust to this noise and can achieve weak/exact recovery in explicit regimes.
We consider the stochastic block model where connection between vertices is perturbed by some latent (and unobserved) random geometric graph. The objective is to prove that spectral methods are robust to this type of noise, even if they are agnostic to the presence (or not) of the random graph. We provide explicit regimes where the second eigenvector of the adjacency matrix is highly correlated to the true community vector (and therefore when weak/exact recovery is possible). This is possible thanks to a detailed analysis of the spectrum of the latent random graph, of its own interest.