Wang Huan, Ma Chuang, Chen Han-Shuang, Lai Ying-Cheng, Zhang Hai-Feng
The Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Science, Anhui University, Hefei, 230601, China.
School of Internet, Anhui University, Hefei, 230601, China.
Nat Commun. 2022 Jun 1;13(1):3043. doi: 10.1038/s41467-022-30706-9.
Previous efforts on data-based reconstruction focused on complex networks with pairwise or two-body interactions. There is a growing interest in networks with higher-order or many-body interactions, raising the need to reconstruct such networks based on observational data. We develop a general framework combining statistical inference and expectation maximization to fully reconstruct 2-simplicial complexes with two- and three-body interactions based on binary time-series data from two types of discrete-state dynamics. We further articulate a two-step scheme to improve the reconstruction accuracy while significantly reducing the computational load. Through synthetic and real-world 2-simplicial complexes, we validate the framework by showing that all the connections can be faithfully identified and the full topology of the 2-simplicial complexes can be inferred. The effects of noisy data or stochastic disturbance are studied, demonstrating the robustness of the proposed framework.
以往基于数据的重建工作主要集中在具有成对或两体相互作用的复杂网络上。人们对具有高阶或多体相互作用的网络兴趣日益浓厚，这就需要基于观测数据来重建此类网络。我们开发了一个结合统计推断和期望最大化的通用框架，以便根据来自两种离散状态动力学的二元时间序列数据，全面重建具有两体和三体相互作用的2 - 单纯复形。我们进一步阐述了一种两步方案，以提高重建精度，同时显著降低计算量。通过合成和真实世界的2 - 单纯复形，我们验证了该框架，表明所有连接都能被准确识别，并且可以推断出2 - 单纯复形的完整拓扑结构。我们还研究了噪声数据或随机干扰的影响，证明了所提出框架的稳健性。
