Gaussian mixture model based reconstruction of undirected networks

Abstract

The reconstruction of network structure from data represents a significant scientific challenge in the field of complex networks, which has attracted considerable attention from the research community. The most of existing network reconstruction methods transform the problem into a series of linear equation systems, to solve the equations. Subsequently, truncation methods are used to determine the local structure of each node by truncating the solution of each equation system. However, truncation methods frequently exhibit inadequate accuracy, and lack methods of evaluating the truncatability of solutions to each system of equations, that is to say, the reconstructability of nodes. In order to address these issues, in this work an undirected network reconstruction method is proposed based on a Gaussian mixture model. In this method, a Gaussian mixture model is first used to cluster the solution results obtainedby solving a series of linear equations, and then the probabilities of the clustering results are utilized to depict the likelihood of connections between nodes. Subsequently, an index of reconstructibility is defined based on information entropy, thus the probability of connections between each node and other nodes can be used to measure the reconstructibility of each node. The proposed method is ultimately applied to undirected networks. Nodes identified with high reconstructibility are used as a training set to guide the structural inference of nodes with lower reconstrucibility, thus enhancing the reconstruction of the undirected network. The symmetrical properties of the undirected network are then employed to infer the connection probabilities of the remaining nodes with other nodes. The experiments on both synthetic and real data are conducted and a variety of methods are used for constructing linear equations and diverse dynamical models. Compared with the results from a previous truncated reconstruction method, the reconstruction outcomes are evaluated. The experimental results show that the method proposed in this work outperforms existing truncation reconstruction methods in terms of reconstruction performance, thus confirming the universality and effectiveness of the proposed method.