Latent structure blockmodels for Bayesian spectral graph clustering

TL;DR

This paper introduces latent structure block models (LSBMs) for Bayesian spectral graph clustering, effectively capturing community-specific one-dimensional manifold structures in network embeddings, and demonstrating strong performance on simulated and real data.

Contribution

The paper proposes LSBMs that explicitly model community-specific manifold structures in spectral embeddings, enhancing clustering accuracy in networks with latent submanifold communities.

Findings

Successfully recovers communities in one-dimensional manifolds

Performs well on both simulated and real-world networks

Achieves accurate community detection without knowing the manifold form

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