论文标题
通过分析曲率来识别网络模型的潜在空间几何形状
Identifying the latent space geometry of network models through analysis of curvature
论文作者
论文摘要
建模网络的一种常见方法将每个节点分配给在低维流形上的位置，其中距离与连接可能性成反比。更积极的流形曲率会鼓励更多和更紧密的社区。负弯曲会引起排斥。我们始终从简单地连接的，完整的riemannian流形的恒定曲率歧管中估算歧管类型，维度和曲率。我们根据集团之间的关系表示该图为嘈杂的距离矩阵，然后开发假设检验，以确定观察到的距离是否可以合可能地嵌入等距离嵌入在每个候选几何形状中。我们将我们的方法应用于经济学和神经科学的数据集。
A common approach to modeling 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 data-sets from economics and neuroscience.
