论文标题
使用曲折的持久性的时间网络分析
Temporal Network Analysis Using Zigzag Persistence
论文作者
论文摘要
这项工作为使用曲折持久性研究时间网络提供了一个框架，这是拓扑数据分析（TDA）领域的工具。最终的方法是一般的，适用于各种时变图形。例如，这些图可能对应于模拟的系统，该系统具有边缘，其权重是时间的函数，或者它们可能代表复杂动力学系统的时间序列。我们使用简单的复合物来表示时间网络的快照，然后可以使用锯齿形持久性来分析这些快照。我们展示了我们的方法在动态网络中的两种应用：对多个时间尺度上的通勤趋势的分析，例如，在大不列颠运输网络中的每日和每周，以及由于以时间序列分区网络代表的动态系统中的周期性/混乱过渡的检测。我们的发现表明，由此产生的零和一维的曲折持续图可以检测到传统连通性和中心图统计信息所遗漏的网络形状的变化。
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.
