Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI, 48824, USA.
Institute for Quantitative Health Science and Engineering, Michigan State University, East Lansing, MI, 48824, USA.
Sci Rep. 2021 Mar 11;11(1):5623. doi: 10.1038/s41598-021-84838-x.
Temporal behavior is an essential aspect of all biological systems. Time series have been previously represented as networks. Such representations must address two fundamental problems on how to: (1) Create appropriate networks to reflect the characteristics of biological time series. (2) Detect characteristic dynamic patterns or events as network temporal communities. General community detection methods use metrics comparing the connectivity within a community to random models, or are based on the betweenness centrality of edges or nodes. However, such methods were not designed for network representations of time series. We introduce a visibility-graph-based method to build networks from time series and detect temporal communities within these networks. To characterize unevenly sampled time series (typical of biological experiments), and simultaneously capture events associated to peaks and troughs, we introduce the Weighted Dual-Perspective Visibility Graph (WDPVG). To detect temporal communities in individual signals, we first find the shortest path of the network between start and end nodes, identifying high intensity nodes as the main stem of our community detection algorithm that act as hubs for each community. Then, we aggregate nodes outside the shortest path to the closest nodes found on the main stem based on the closest path length, thereby assigning every node to a temporal community based on proximity to the stem nodes/hubs. We demonstrate the validity and effectiveness of our method through simulation and biological applications.
时间行为是所有生物系统的一个重要方面。时间序列以前被表示为网络。这种表示必须解决两个基本问题：（1）创建适当的网络来反映生物时间序列的特征。（2）检测作为网络时间社区的特征动态模式或事件。一般的社区检测方法使用比较社区内连接性与随机模型的度量，或者基于边或节点的中间中心性。然而，这些方法不是为时间序列的网络表示而设计的。我们引入了一种基于可见性图的方法，从时间序列中构建网络，并在这些网络中检测时间社区。为了描述不均匀采样的时间序列（典型的生物实验），同时捕捉与峰值和低谷相关的事件，我们引入了加权双视角可见性图（WDPVG）。为了在单个信号中检测时间社区，我们首先找到网络中起始和结束节点之间的最短路径，将高强度节点识别为我们社区检测算法的主干，作为每个社区的枢纽。然后，我们根据最短路径长度，将最短路径之外的节点聚集到主干上最近的节点，从而根据与主干节点/枢纽的接近程度将每个节点分配到一个时间社区。我们通过模拟和生物应用证明了我们方法的有效性和有效性。
