Link prediction by deep non-negative matrix factorization

Link prediction aims to predict missing links or eliminate spurious links and new links in future network by known network structure information. Most existing link prediction methods are shallow models and did not consider network noise. To address these issues, in this paper, we propose a novel link prediction model based on deep non-negative matrix factorization, which elegantly fuses topology and sparsity-constrained to perform link prediction tasks. Specifically, our model fully exploits the observed link information for each hidden layer by deep non-negative matrix factorization. Then, we utilize the common neighbor method to calculate the similarity scores and map it to multi-layer low-dimensional latent space to obtain the topological information of each hidden layer. Simultaneously, we employ the l(2,1)-norm constrained factor matrix at each hidden layer to remove the random noise. Besides, we provide an effective the multiplicative updating rules to learn the parameter of this model with the convergence guarantees. Extensive experiments results on eight real-world datasets demonstrate that our proposed model significantly outperforms the state-of-the-art methods.