Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks

Link prediction is one of the most widely studied problems in the area of complex network analysis, in which machine learning techniques can be applied to deal with it. The biggest drawback of the existing methods, however, is that in most cases they only consider the topological structure of the network, and therefore completely miss out on the great potential that stems from the nodal attributes. Both topological structure and nodes’ attributes are essential in predicting the evolution of attributed networks and can act as complements to each other. To bring out their full potential in solving the link prediction problem, a novel Robust Graph Regularization Nonnegative Matrix Factorization for Attributed Networks (RGNMF-AN) was proposed, which models not only the topology structure of networks but also their node attributes for direct link prediction. This model, in particular, combines two types of information, namely network topology, and nodal attributes information, and calculates high-order proximities between nodes using the Structure-Attribute Random Walk Similarity (SARWS) method. The SARWS score matrix is an indicator structural and attributed matrix that collects more useful attributed information in high-order proximities, whereas graph regularization technology combines the SARWS score matrix with topological and attribute information to collect more valuable attributed information in high-order proximities. Furthermore, the RGNMF-AN employs the ℓ_2,1-norm to constrain the loss function and regularization terms, effectively removing random noise and spurious links. According to empirical findings on nine real-world complex network datasets, the use of a combination of attributed and topological information in tandem enhances the prediction performance significantly compared to the baseline and other NMF-based algorithms.