基于双曲和球面几何的潜在空间网络建模
Latent Space Network Modelling with Hyperbolic and Spherical Geometries
摘要：
一个丰富的网络模型将每个节点与一个低维潜在坐标相关联，该坐标控制着连接形成的倾向。这种类型的模型在网络分析文献中得到了很好的建立，其中通常假设基础几何是欧几里得的。最近的工作探讨了这种选择的后果，并激发了依赖于非欧几里德潜在几何模型的研究，主要集中在球面和双曲几何。在本文中，我们研究在何种程度上可以从网络中的可观察链接推断出潜在的功能，考虑依赖于球形和双曲几何的网络模型。对于每一个几何形状，我们描述了一个潜在的空间网络模型，详细的限制，消除了众所周知的可识别性问题的潜在坐标，并提出贝叶斯估计方案。因此，我们开发的计算程序来执行推理的网络模型中，底层几何的属性起着至关重要的作用。最后，我们评估这些模型的真实数据的有效性。
英文摘要：
A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is typical to assume that the underlying geometry is Euclidean. Recent work has explored the consequences of this choice and has motivated the study of models which rely on non-Euclidean latent geometries, with a primary focus on spherical and hyperbolic geometry. In this paper, we examine to what extent latent features can be inferred from the observable links in the network, considering network models which rely on spherical and hyperbolic geometries. For each geometry, we describe a latent space network model, detail constraints on the latent coordinates which remove the well-known identifiability issues, and present Bayesian estimation schemes. Thus, we develop computational procedures to perform inference for network models in which the properties of the underlying geometry play a vital role. Finally, we assess the validity of these models on real data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
