Ma Chuang, Zhang Hai-Feng, Lai Ying-Cheng
School of Mathematical Science, Anhui University, Hefei 230601, China.
Center of Information Support &Assurance Technology, Anhui University, Hefei 230601, China.
Phys Rev E. 2017 Aug;96(2-1):022320. doi: 10.1103/PhysRevE.96.022320. Epub 2017 Aug 25.
In the real world there are situations where the network dynamics are transient (e.g., various spreading processes) and the final nodal states represent the available data. Can the network topology be reconstructed based on data that are not time series? Assuming that an ensemble of the final nodal states resulting from statistically independent initial triggers (signals) of the spreading dynamics is available, we develop a maximum likelihood estimation-based framework to accurately infer the interaction topology. For dynamical processes that result in a binary final state, the framework enables network reconstruction based solely on the final nodal states. Additional information, such as the first arrival time of each signal at each node, can improve the reconstruction accuracy. For processes with a uniform final state, the first arrival times can be exploited to reconstruct the network. We derive a mathematical theory for our framework and validate its performance and robustness using various combinations of spreading dynamics and real-world network topologies.
在现实世界中，存在网络动态是瞬态的情况（例如，各种传播过程），并且最终的节点状态代表可用数据。能否基于非时间序列的数据重建网络拓扑结构？假设可以获得由传播动态的统计独立初始触发（信号）产生的最终节点状态的集合，我们开发了一个基于最大似然估计的框架来准确推断相互作用拓扑。对于导致二元最终状态的动态过程，该框架能够仅基于最终节点状态进行网络重建。诸如每个信号在每个节点的首次到达时间等附加信息，可以提高重建精度。对于具有均匀最终状态的过程，可以利用首次到达时间来重建网络。我们为我们的框架推导了一个数学理论，并使用传播动态和现实世界网络拓扑的各种组合验证了其性能和鲁棒性。
