Latent structure blockmodels for Bayesian spectral graph clustering

Abstract Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph generated from a latent position model. Furthermore, presence communities within might generate community-specific structures in embedding, but this not explicitly accounted for most statistical models networks. article, class called structure block (LSBM) proposed address such scenarios, allowing clustering one-dimensional manifold present. LSBMs focus on specific space model, random dot product (RDPG), and assign positions each community. A Bayesian model embeddings arising discussed, shown have good performance simulated real-world data. The able correctly recover underlying manifold, even parametric form curves unknown, achieving remarkable results variety real