Detection of Model-based Planted Pseudo-cliques in Random Dot Product Graphs by the Adjacency Spectral Embedding and the Graph Encoder Embedding

In this paper, we explore the capability of both the Adjacency Spectral Embedding (ASE) and the Graph Encoder Embedding (GEE) for capturing an embedded pseudo-clique structure in the random dot product graph setting. In both theory and experiments, we demonstrate that this pairing of model and methods can yield worse results than the best existing spectral clique detection methods, demonstrating at once the methods' potential inability to capture even modestly sized pseudo-cliques and the methods' robustness to the model contamination giving rise to the pseudo-clique structure. To further enrich our analysis, we also consider the Variational Graph Auto-Encoder (VGAE) model in our simulation and real data experiments.