Detection of Model-Based Planted Pseudo-Cliques in Random Dot Product Graphs by the Adjacency Spectral Embedding and the Graph Encoder Embedding.

Abstract

In this article, 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, in the absence of additional clean (i.e., without the implanted pseudo-clique) network data, this pairing of model and methods can yield worse results than the best existing spectral clique detection methods. However, these methods can be used to asymptotically localize the pseudo-cliques if additional clean, independent network data is provided. This demonstrates at once the methods' potential ability/inability to capture 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.