Identifying the latent space geometry of network models through analysis of curvature
该研究提出一种方法，从常曲率黎曼流形中一致估计网络节点的潜在空间类型、维度和曲率，通过分析团之间的连接构建噪声距离矩阵，并开发假设检验判断观测距离能否等距嵌入候选几何空间，应用于经济学和神经科学数据集。
Abstract 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.