Popularity Adjusted Block Models are Generalized Random Dot Product Graphs. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Koo, John; Tang, Minh; Trosset, Michael W.
• Is Part Of: Journal of computational and graphical statistics. Volume 32:Issue 1(2023)
• Page Start: 131
• Page End: 144
• Publication Date: 2023-01-02
• Subjects: Block models -- Community detection -- Generalized random dot product graphs -- Network analysis -- Sparse subspace clustering; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2022.2081576
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors. This insight allows us to construct new algorithms for community detection and parameter estimation for the PABM, as well as improve an existing algorithm that relies on Sparse Subspace Clustering. Using established asymptotic properties of Adjacency Spectral Embedding for the GRDPG, we derive asymptotic properties of these algorithms. In particular, we demonstrate that the absolute number of community detection errors tends to zero as the number of graph vertices tends to infinity. Simulation experiments illustrate these properties. Supplementary materials for this article are available online.