Full reconstruction of simplicial complexes from binary contagion and Ising data

• Published in: Nature communications Vol. 13; no. 1; p. 3043
• Main Authors: Wang, Huan, Ma, Chuang, Chen, Han-Shuang, Lai, Ying-Cheng, Zhang, Hai-Feng
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.06.2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/705/1041; 639/766/530/2801; Binary data; Computer applications; Data recovery; Graphs; Humanities and Social Sciences; Inverse problems; Ising model; Many body problem; multidisciplinary; Networks; Reconstruction; Science; Science (multidisciplinary); Statistical analysis; Statistical inference; Stochasticity; Time series; Topology
• ISSN: 2041-1723; 2041-1723
• 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. Data-driven recovery of topology is challenging for networks beyond pairwise interactions. The authors propose a framework to reconstruct complex networks with higher-order interactions from time series, focusing on networks with 2-simplexes where social contagion and Ising dynamics generate binary data.