🤖 AI Summary
This paper investigates pseudo-clique detection in random dot product graphs (RDPGs), focusing on the ability of adjacency spectral embedding (ASE) and graph encoder embedding (GEE) to identify model-injected pseudo-cliques in the absence of clean auxiliary network data. Theoretically and empirically, both ASE and GEE underperform the optimal spectral method for detecting medium-sized pseudo-cliques, revealing fundamental performance limits; yet surprisingly, they exhibit strong robustness against model contamination induced by pseudo-clique generation—challenging the conventional assumption of universal superiority for spectral methods. Moreover, when independent clean network data become available, ASE and GEE achieve asymptotically consistent pseudo-clique localization. This work provides the first systematic characterization of the coexistence of failure and robustness in embedding-based methods under structural contamination, offering new theoretical foundations and practical insights for using graph embeddings in subgraph discovery.
📝 Abstract
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.
