Reconstruction of undirected networks based on Gaussian mixture model

Abstract

The reconstruction of network structure from data represents a significant scientific challenge in the field of complex networks, and has attracted considerable attention from the research community. The majority of existing network reconstruction methods transform the problem into a series of linear equation systems, which are then solved. Subsequently, truncation methods are employed to determine the local structure of each node by truncating the solutions of each equation system. However, these truncation methods frequently exhibit inadequate accuracy, and there is a paucity of methods for evaluating the truncatability of solutions to each system of equations, that is to say, the reconstructability of nodes. In order to address these issues, this paper proposes an undirected network reconstruction method based on a Gaussian mixture model. The method initially employs a Gaussian mixture model to cluster the solution results obtained from solving a series of linear equations. It then employs the probabilities of the clustering results to depict the likelihood of connections between nodes. Subsequently, an index of reconstructibility is defined based on information entropy, whereby the probability of connections between each node and other nodes is employed to measure the reconstructibility of each node. The proposed method is finally applied to undirected networks, with nodes identified as having high reconstructibility and the connection probabilities of these nodes with others used as a training set. The symmetrical properties of the undirected network are then employed to infer the connection probabilities of the remaining nodes with other nodes. In the experimental section, experiments were conducted on both synthetic and real data, utilising a variety of methods for constructing linear equations and diverse dynamical models. The reconstruction outcomes were evaluated in comparison with those of a previous truncated reconstruction method. The experimental results demonstrate that the method proposed in this paper exhibits superior reconstruction performance to the previous truncated reconstruction method, thereby substantiating the universality and effcacy of the proposed approach.