论文标题
对局部潜在网络曲率的渐近正常估计
Asymptotically Normal Estimation of Local Latent Network Curvature
论文作者
论文摘要
网络数据通常在整个物理，社会和生物科学中使用，由节点（个体）和它们之间的边缘（相互作用）组成。表示网络数据复杂的高维结构的一种方法是将图嵌入到低维几何空间中。特别是该空间的曲率提供了有关图中结构的见解，例如形成三角形或类似树状结构的倾向。我们根据三角侧长度和对方角的侧点的中点的长度得出曲率的估计函数。我们构造一个估计器，其中唯一的输入是距离矩阵，还建立了渐近正态性。接下来，我们为网络引入了一种新型的潜在距离矩阵估计器和一种有效的算法，以通过求解迭代二次程序来计算估计值。我们将此方法应用于Los Alamos国家实验室统一网络和主机数据集，并显示曲率估计值如何比NAIVE方法更快地检测红线攻击，并在物理学中发现非稳态潜在曲率。本文的代码可在https://github.com/stevejwr/netcurve上获得，该方法可在r软件包中实现https://github.com/stevejwr/lolar。
Network data, commonly used throughout the physical, social, and biological sciences, consist of nodes (individuals) and the edges (interactions) between them. One way to represent network data's complex, high-dimensional structure is to embed the graph into a low-dimensional geometric space. The curvature of this space, in particular, provides insights about the structure in the graph, such as the propensity to form triangles or present tree-like structures. We derive an estimating function for curvature based on triangle side lengths and the length of the midpoint of a side to the opposing corner. We construct an estimator where the only input is a distance matrix and also establish asymptotic normality. We next introduce a novel latent distance matrix estimator for networks and an efficient algorithm to compute the estimate via solving iterative quadratic programs. We apply this method to the Los Alamos National Laboratory Unified Network and Host dataset and show how curvature estimates can be used to detect a red-team attack faster than naive methods, as well as discover non-constant latent curvature in co-authorship networks in physics. The code for this paper is available at https://github.com/SteveJWR/netcurve, and the methods are implemented in the R package https://github.com/SteveJWR/lolaR.
