论文标题
网络的几何抽样
Geometric Sampling of Networks
论文作者
论文摘要
由基于RICCI曲率采样的方法和结果的动机，我们提出了类似的网络方法。为此，我们可以吸引三种类型的离散曲率，即用于基于边缘和基于节点的采样的图形，完整的Forman-和Haantjes-Ricci曲线。我们介绍了现实生活网络以及图像处理中产生的方格的实验结果。此外，我们考虑安装RICCI流，并使用它们来检测网络的骨干。我们还开发了与Forman-Ricci曲率相关的嵌入核，并使用它们来检测网络的粗糙结构，以及使用应用程序的应用程序可视化网络可视化。还研究了原始歧管的RICCI曲率与RICCI曲率驱动离散化之间的关系。
Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks. To this end we make appeal to three types of discrete curvature, namely the graph Forman-, full Forman- and Haantjes-Ricci curvatures for edge-based and node-based sampling. We present the results of experiments on real life networks, as well as for square grids arising in Image Processing. Moreover, we consider fitting Ricci flows and we employ them for the detection of networks' backbone. We also develop embedding kernels related to the Forman-Ricci curvatures and employ them for the detection of the coarse structure of networks, as well as for network visualization with applications to SVM. The relation between the Ricci curvature of the original manifold and that of a Ricci curvature driven discretization is also studied.
