Reconstructing Network Structures Using Gaussian Mixture Model: From Unsigned to Signed Networks

Network reconstruction, which involves inferring a network’s topology from observational data, is a critical challenge in network science. Because observational data are often limited, prior knowledge is often employed to enhance the accuracy of network reconstruction, including constraints related to sparsity, symmetry, or network dynamics. In many cases, we may possess prior knowledge regarding the number of types of edges within networks, yet the specific solutions of these types of edges remain unknown. For instance, while it is evident that two types of edges (i.e., positive and negative) exist in signed networks, the possible solution for each edge type is frequently unclear, rendering existing methods, such as the signal Lasso approach, ineffective. In this work, to effectively leverage this readily available prior knowledge, we propose a novel network reconstruction framework based on the Gaussian mixture model (GMM), which integrates Bayesian models and employs the GMM to model the distribution of unknown edges as prior probabilities. The method is effective for both unsigned and signed networks and achieves high accuracy even with limited prior information, without requiring specific solutions for each edge type, particularly in cases of network sparsity or noisy data.