Nonnegative matrix factorization for link prediction in directed complex networks using PageRank and asymmetric link clustering information

•Introduce a model to fuse local and global information in directed network.•The model can capture topological structures and robust to sparser networks.•Present an effective update rule to learn model parameters.•Experimental results show that our method is outperforms other indices. The aim of link prediction is to predict missing links in current networks or new links in future networks. Almost all the existing directed link prediction algorithms only take into account the links direction formation but ignored the abundant network topological information such as local and global structures. Therefore, how to preserve both local and global structure information is an important issue for directed link prediction. To solve this problem, in this paper, we are motivated to propose a novel Nonnegative Matrix Factorization via Asymmetric link clustering and PageRank model, namely NMF-AP. Specifically, we utilize the PageRank algorithm to calculate the influence score of the node, which captures the global network structure information. While we employ the asymmetric link clustering method to calculate the link clustering coefficient score, which preserves the local network structure information. By jointly optimizing them in the nonnegative matrix factorization model, our model can preserve both the local and global information at the same time. Besides, we provide an effective the multiplicative updating rules to learn the parameter of NMF-AP. Extensive experiments are conducted on ten real-world directed networks, experiment results demonstrate that the method NMF-AP outperforms state-of-the-art link prediction methods.