论文标题
独立于模型的方法，用于将定向网络嵌入欧几里得和双曲线空间
Model-independent methods for embedding directed networks into Euclidean and hyperbolic spaces
论文作者
论文摘要
双曲线空间中网络节点的布置已成为一个广泛研究的问题，这是由于许多结果，表明复杂网络结构背后存在隐藏的度量空间。尽管已经开发了几种方法来嵌入无向网络的双曲线嵌入，但能够处理有向网络的方法仍处于起步阶段。在这里，我们提出了一个基于反映网络拓扑的接近度矩阵的尺寸的框架，再加上将欧几里得节点坐标转换为双曲线网络的一般转换方法，即使对于有向网络也是如此。在提出一种新的接近度度量的同时，我们还将早期的欧几里得嵌入方法纳入了我们的管道中，这证明了我们的欧几里得 - 氧化体转换的广泛适用性。此外，我们引入了一种降低尺寸的技术，该技术将节点直接映射到双曲线空间中，目的是重现在给定（UN）定向网络上测得的距离矩阵。根据映射精度，图形重建性能和贪婪的路由得分，我们的方法能够为多个真实网络生成高质量的嵌入。
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods have already been developed for the hyperbolic embedding of undirected networks, approaches able to deal with directed networks are still in their infancy. Here, we propose a framework based on the dimension reduction of proximity matrices reflecting the network topology, coupled with a general conversion method transforming Euclidean node coordinates into hyperbolic ones even for directed networks. While proposing a new measure of proximity, we also incorporate an earlier Euclidean embedding method in our pipeline, demonstrating the widespread applicability of our Euclidean-hyperbolic conversion. Besides, we introduce a dimension reduction technique that maps the nodes directly into the hyperbolic space with the aim of reproducing a distance matrix measured on the given (un)directed network. According to mapping accuracy, graph reconstruction performance and greedy routing score, our methods are capable of producing high-quality embeddings for several real networks.
