论文标题
随机几何图：一些最新的发展和观点
Random Geometric Graph: Some recent developments and perspectives
论文作者
论文摘要
随机几何图（RGG）是具有基础空间表示的网络数据的随机图模型。几何形状赋予RGGS具有丰富的依赖性结构，并且通常会导致现实世界网络（例如小世界现象和聚类）的理想特性。 RGG最初引入了模型无线通信网络，现在非常受欢迎，其应用程序从网络用户分析到生物学中的蛋白质 - 蛋白质相互作用。 RGG也纯粹具有理论上的兴趣，因为潜在的几何形状引起了具有挑战性的数学问题。他们的决议涉及概率，统计，组合学或信息理论的结果，将RGGS放置在大量研究社区的交汇处。本文从高维度和非参数推断的镜头中调查了RGGS的最新发展。我们还解释了该模型与基于古典社区的随机图模型有何不同，我们回顾了最近尝试将两全其美的作品。作为副产品，我们揭示了证明中使用的数学工具的范围。
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such as the small-world phenomenon and clustering. Originally introduced to model wireless communication networks, RGGs are now very popular with applications ranging from network user profiling to protein-protein interactions in biology. RGGs are also of purely theoretical interest since the underlying geometry gives rise to challenging mathematical questions. Their resolutions involve results from probability, statistics, combinatorics or information theory, placing RGGs at the intersection of a large span of research communities. This paper surveys the recent developments in RGGs from the lens of high dimensional settings and non-parametric inference. We also explain how this model differs from classical community based random graph models and we review recent works that try to take the best of both worlds. As a by-product, we expose the scope of the mathematical tools used in the proofs.
