Latent structure blockmodels for Bayesian spectral graph clustering

• Published in: arXiv.org
• Main Authors: Francesco Sanna Passino, Heard, Nicholas A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 02.01.2022
• Subjects: Bayesian analysis; Clustering; Computer Science - Learning; Embedding; Manifolds (mathematics); Statistical models; Statistics - Machine Learning
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2107.01734

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.