Shi Rundong, Jiang Weinuo, Wang Shihong
School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Chaos. 2020 Jan;30(1):013138. doi: 10.1063/1.5127052.
Depicting network structures from measurable data is of significance. In real-world situations, it is common that some variables of networks are unavailable or even unknown. These unavailable and unknown variables, i.e., hidden variables, will lead to much reconstruction error, even make reconstruction methods useless. In this paper, to solve hidden variable problems, we propose three reconstruction methods, respectively, based on the following conditions: statistical characteristics of hidden variables, linearizable hidden variables, and white noise injection. Among them, the method based on white noise injection is active and invasive. In our framework, theoretic analyses of these three methods are given at first, and, furthermore, the validity of theoretical derivations and the robustness of these methods are fully verified through numerical results. Our work may be, therefore, helpful for practical experiments.
从可测量数据中描绘网络结构具有重要意义。在现实世界中，网络的某些变量不可用甚至未知是很常见的。这些不可用和未知的变量，即隐藏变量，会导致大量的重构误差，甚至使重构方法失效。在本文中，为了解决隐藏变量问题，我们分别基于隐藏变量的统计特征、可线性化隐藏变量和白噪声注入这三个条件提出了三种重构方法。其中，基于白噪声注入的方法是主动且侵入性的。在我们的框架中，首先对这三种方法进行了理论分析，此外，通过数值结果充分验证了理论推导的有效性和这些方法的鲁棒性。因此，我们的工作可能对实际实验有所帮助。
