Robust non-negative matrix factorization for link prediction in complex networks using manifold regularization and sparse learning

The aim of link prediction is to disclose the underlying evolution mechanism of networks, which could be utilized to predict missing links or eliminate spurious links. However, real-world networks data usually encounters challenges,such as missing links, spurious links and random noise, which seriously hamper the prediction accuracy of existing link prediction methods. Therefore, in this paper, we propose a novel Robust Non-negative Matrix Factorization via jointly Manifold regularization and Sparse learning (MS-RNMF) method in link prediction that solves the problems. Compared to existing methods, MS-RNMF has three-fold advantages: First of all, the MS-RNMF employ manifold regularization and k-medoids algorithm jointly to preserve the network local and global topology information. Besides, the MS-RNMF adopts ℓ2,1-norm to constrain loss function and regularization term, random noise and spurious links could be effectively remove. Finally, we employ multiplicative updating rules to learn the model parameter and prove the convergence of the algorithm. Extensive experiments results performed on eleven real-world networks demonstrate that the MS-RNMF outperforms the state-of-the-arts methods in predicting missing links , identifying spurious links and eliminating random noise.