Network Topology Inference from Heterogeneous Incomplete Graph Signals

Inferring network topologies from observed graph-structured data (also known as graph signals) is a crucial task in many applications of network science. Existing papers on network topology inference typically assume that the observations at all nodes are available. However, there are many situations where only partial observations can be collected due to application-specific constraints. To handle the missing data problem, we propose a framework that relies on heterogeneous incomplete data from a collection of related networks to identify multiple network topologies simultaneously. This work advocates the Gaussian graphical model (GGM) and casts the topology inference problem in terms of estimating the precision matrix that has a form of graph Laplacian. Firstly, an unbiased estimator for the covariance matrix of incomplete data is established and then algorithms based on the alternating direction method of multipliers (ADMM) are developed to jointly estimate graph topologies, rather than estimate each graph topology separately. So that we can borrow information across the multiple related networks to eliminate the impact of missing data. Moreover, non-asymptotic statistical analysis is provided, which proves the consistency of the graph estimator and enables us to investigate the effect of several key factors on the graph estimation error bound. Furthermore, based on the consistent graph estimator, an adaptive algorithm that utilizes the reweighting scheme is proposed to improve the estimation accuracy of the graph-edge structure. Finally, we evaluate our method on both real and synthetic datasets, and the experimental results demonstrate the advantage of our method in comparison with benchmarking algorithms.