Characterizing Distances of Networks on the Tensor Manifold
Characterizing Distances of Networks on the Tensor Manifold
复制标题
在张量流形上表征网络距离
DOI：
10.1007/978-3-030-36687-2_79
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Sandhu, Romeil
中科院分区：
文献类型：
--
作者：
Islam, Bipul;Liu, Ji;Sandhu, Romeil
理解动态系统的核心是维护和控制系统行为的能力，包括鲁棒性，异质性和/或状态转移检测的概念。最近，为了探索这样的功能特性，一个方便的表示方法是将这样的动态系统建模为由有限但数量非常大的相互作用的代理组成的加权图。也就是说，存在非常有限的相关统计理论，能够科普现实生活中的数据，即，如何在与特定网络或网络到网络变化相对的网络“族”上执行分析和/或统计。在这里，我们感兴趣的是网络族的分析，其中每个网络代表一个“点”的基础统计流形。要做到这一点，我们探讨了黎曼结构的张量流形开发的Pennec以前适用于扩散张量成像（DTI）对网络分析的问题。特别是，虽然本说明的重点是Pennec定义的“测地线”之间的一个家庭的网络，我们将展示它如何奠定了基础，为今后的工作，发展措施的网络鲁棒性的政权转移检测。最后，我们的实验突出了建议的距离合成网络和生物（干细胞）系统的应用。
At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, and/or regime-shift detection. Recently, to explore such functional properties, a convenient representation has been to model such dynamical systems as a weighted graph consisting of a finite, but very large number of interacting agents. This said, there exists very limited relevant statistical theory that is able cope with real-life data, i.e., how does perform analysis and/or statistics over a “family” of networks as opposed to a specific network or network-to-network variation. Here, we are interested in the analysis of network families whereby each network represents a “point” on an underlying statistical manifold. To do so, we explore the Riemannian structure of the tensor manifold developed by Pennec previously applied to Diffusion Tensor Imaging (DTI) towards the problem of network analysis. In particular, while this note focuses on Pennec definition of “geodesics” amongst a family of networks, we show how it lays the foundation for future work for developing measures of network robustness for regime-shift detection. We conclude with experiments highlighting the proposed distance on synthetic networks and an application towards biological (stem-cell) systems.
影响因子：
13.6
作者：
Sandhu RS;Georgiou TT;Tannenbaum AR
通讯作者：
Tannenbaum AR
影响因子：
0.8
作者：
Ollivier, Yann
通讯作者：
Ollivier, Yann