Zhang Yichi, Li Yonggang, Deng Wenfeng, Huang Keke, Yang Chunhua
School of Automation, Central South University, Changsha 410083, China.
Chaos. 2021 Jan;31(1):013107. doi: 10.1063/5.0031134.
Identification of complex networks from limited and noise contaminated data is an important yet challenging task, which has attracted researchers from different disciplines recently. In this paper, the underlying feature of a complex network identification problem was analyzed and translated into a sparse linear programming problem. Then, a general framework based on the Bayesian model with independent Laplace prior was proposed to guarantee the sparseness and accuracy of identification results after analyzing influences of different prior distributions. At the same time, a three-stage hierarchical method was designed to resolve the puzzle that the Laplace distribution is not conjugated to the normal distribution. Last, the variational Bayesian was introduced to improve the efficiency of the network reconstruction task. The high accuracy and robust properties of the proposed method were verified by conducting both general synthetic network and real network identification tasks based on the evolutionary game dynamic. Compared with other five classical algorithms, the numerical experiments indicate that the proposed model can outperform these methods in both accuracy and robustness.
从有限且受噪声污染的数据中识别复杂网络是一项重要但具有挑战性的任务，该任务最近吸引了来自不同学科的研究人员。本文分析了复杂网络识别问题的潜在特征，并将其转化为一个稀疏线性规划问题。然后，在分析不同先验分布的影响后，提出了一个基于具有独立拉普拉斯先验的贝叶斯模型的通用框架，以保证识别结果的稀疏性和准确性。同时，设计了一种三阶段分层方法来解决拉普拉斯分布与正态分布不共轭的难题。最后，引入变分贝叶斯方法以提高网络重建任务的效率。通过基于进化博弈动态进行一般合成网络和真实网络识别任务，验证了所提方法的高精度和鲁棒性。与其他五种经典算法相比，数值实验表明所提模型在准确性和鲁棒性方面均优于这些方法。
