Identifying the latent space geometry of network models through analysis of curvature

• 成果类型: Article
• 署名作者: Lubold, Shane; Chandrasekhar, Arun G.; McCormick, Tyler H.
• 署名单位: University of Washington; University of Washington Seattle; Stanford University; National Bureau of Economic Research; University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad002
• 发表日期: 2023
• 页码: 240-292
• 关键词: Social networks; Financial networks; RISK; eigenvalues; arrays; graphs

摘要

A common approach to modelling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter communities; negative curvature induces repulsion. We consistently estimate manifold type, dimension, and curvature from simply connected, complete Riemannian manifolds of constant curvature. We represent the graph as a noisy distance matrix based on the ties between cliques, then develop hypothesis tests to determine whether the observed distances could plausibly be embedded isometrically in each of the candidate geometries. We apply our approach to datasets from economics and neuroscience.