Temporal network analysis using zigzag persistence
Temporal network analysis using zigzag persistence
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DOI：
10.1140/epjds/s13688-023-00379-5
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发表时间：
2022-05
期刊：
影响因子：
3.6
通讯作者：
Audun D. Myers;Firas A. Khasawneh;E. Munch
中科院分区：
文献类型：
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作者：
Audun D. Myers;Firas A. Khasawneh;E. Munch
这项工作提出了一个框架，研究时间网络使用锯齿持久性，从拓扑数据分析（TDA）领域的工具。所得到的方法是通用的，适用于各种各样的时变图。例如，这些图可以对应于被建模为具有其权重是时间的函数的边的网络的系统，或者它们可以表示复杂动态系统的时间序列。我们使用单纯复形来表示时间网络的快照，然后可以使用zigzag持久性进行分析。我们展示了我们的方法在动态网络中的两个应用：在多个时间尺度上分析通勤趋势，例如，每天和每周，在英国的交通网络，和检测周期/混沌过渡，由于在动态系统的时间有序分区网络表示的不稳定性。我们的研究结果表明，由此产生的零维和一维锯齿形持久性图可以检测到传统的连接性和中心性图统计所错过的网络形状的变化。
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For example, these graphs may correspond to a system modeled as a network with edges whose weights are functions of time, or they may represent a time series of a complex dynamical system. We use simplicial complexes to represent snapshots of the temporal networks that can then be analyzed using zigzag persistence. We show two applications of our method to dynamic networks: an analysis of commuting trends on multiple temporal scales, e.g., daily and weekly, in the Great Britain transportation network, and the detection of periodic/chaotic transitions due to intermittency in dynamical systems represented by temporal ordinal partition networks. Our findings show that the resulting zero- and one-dimensional zigzag persistence diagrams can detect changes in the networks’ shapes that are missed by traditional connectivity and centrality graph statistics.