  Based on the binary time series data of social infection dynamics, we propose
a general framework to reconstruct 2-simplex 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
expression. 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. We apply a two-step scheme to improve the effectiveness of network
reconstruction while reducing the amount of computation significantly. The
framework has been tested on different types of complex networks. Among them,
four kinds of networks can obtain high reconstruction effectiveness. Besides,
we study the influence of noise data or random interference and prove the
robustness of the framework, then the effects of two kinds of hyper-parameters
on the experimental results are tested. Finally, we analyze which type of
network is more suitable for this framework, and propose methods to improve the
effectiveness of the experimental results.
