Expectation-maximizing network reconstruction and most applicable network types based on binary time series data

Abstract

Based on the binary time series data of social infection dynamics, we propose a general framework to reconstruct the 2-simplicial complexes with two-body and three-body interactions by combining the maximum likelihood estimation in statistical inference and introducing the expectation maximization. In order to improve the code running efficiency, the whole algorithm adopts vectorization expressions. Through the inference of maximum likelihood estimation, the vectorization expression of the edge existence probability can be obtained, and through the probability matrix, the adjacency matrix of the network can be estimated. The framework has been tested on different types of complex networks. Among them, four kinds of networks achieve high reconstruction effectiveness. Finally, we analyze which type of network is more suitable for this framework, and propose methods to improve the effectiveness of the experimental results. Complex networks are presented in the form of simplicial complexes. In this paper, focusing on the differences in the effectiveness of simplicial complexes reconstruction after the same number of iterations, we innovatively propose that simplex reconstruction based on maximum likelihood estimation is more suitable for small-world networks and three indicators to judge the structural similarity between a network and a small-world network are given. The closer the network structure to the small-world network is, the higher efficiency in a shorter time can be obtained.