Multiscale dynamical embeddings of complex networks
Multiscale dynamical embeddings of complex networks
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DOI：
10.1103/physreve.99.062308
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发表时间：
2019-06-20
影响因子：
2.4
通讯作者：
Barahona, Mauricio
中科院分区：
文献类型：
--
作者：
Schaub, Michael T.;Delvenne, Jean-Charles;Barahona, Mauricio
复杂系统和关系数据通常被抽象为网络上的动态过程。要了解、预测和控制他们的行为，关键的一步是提取对此类网络的简化描述。受控制论思想的启发，我们提出了一种依赖于时间的节点间动态相似性度量，该度量量化了节点输入对网络的影响。这种动态相似性导致了可用于多个分析任务的嵌入。在这里，我们关注(I)降维，即将节点投影到低维空间，以捕捉不同时间尺度的动态相似性，以及(Ii)如何利用我们的嵌入来发现功能模块。我们通过案例研究来举例说明我们的想法，这些案例研究的重点是没有强连通性的有向网络和带符号的网络。我们进一步强调，通过使用这里发展的动力学观点，来自社区检测的某些想法可以被概括并与控制理论联系起来。
Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.