Nonnegative matrix factorization algorithms for link prediction in temporal networks using graph communicability

Networks derived from many disciplines, such as social relations, web contents, and cancer progression, are temporal and incomplete. Link prediction in temporal networks is of theoretical interest and practical significance because spurious links are critical for investigating evolving mechanisms. In this study, we address the temporal link prediction problem in networks, i.e. predicting links at time T+1 based on a given temporal network from time 1 to T. To address the relationships among matrix decomposition-based algorithms, we prove the equivalence between the eigendecomposition and nonnegative matrix factorization (NMF) algorithms, which serves as the theoretical foundation for designing NMF-based algorithms for temporal link prediction. A novel NMF-based algorithm is proposed based on such equivalence. The algorithm factorizes each network to obtain features using graph communicability, and then collapses the feature matrices to predict temporal links. Compared with state-of-the-art methods, the proposed algorithm exhibits significantly improved accuracy by avoiding the collapse of temporal networks. Experimental results of a number of artificial and real temporal networks illustrate that the proposed method is not only more accurate but also more robust than state-of-the-art approaches.