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In this paper, we explore the capability of both the Adjacency SpectralEmbedding (ASE) and the Graph Encoder Embedding (GEE) for capturing an embeddedpseudo-clique structure in the random dot product graph setting. In both theoryand experiments, we demonstrate that this pairing of model and methods canyield worse results than the best existing spectral clique detection methods,demonstrating at once the methods' potential inability to capture even modestlysized pseudo-cliques and the methods' robustness to the model contaminationgiving rise to the pseudo-clique structure. To further enrich our analysis, wealso consider the Variational Graph Auto-Encoder (VGAE) model in our simulationand real data experiments.

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