Kernel framework based on non-negative matrix factorization for networks reconstruction and link prediction

Link prediction aims to extract missing informations, identify spurious interactions and potential informations in complex networks. Similarity-based methods, maximum likelihood methods and probabilistic models are the mainstreaming classes algorithms for link prediction. Meanwhile, low rank matrix approximation has been widely used in networks analysis and it can extract more useful features hidden in the original data through some kernel-induced nonlinear mapping. In this paper, based on the non-negative matrix factorization (NMF), we propose a kernel framework for link prediction and network reconstruction by using different kernels which could get both global and local information of the network through kernel mapping. In detailed, we map the adjacency matrix of the network to another feature space by two kernel functions, the Linear Kernel and Covariance Kernel, which have the principled interpretations for the network analysis and link predication. We test the AUC and Precision of widely used methods on a series of real world networks with different proportions of the training sets, experimental results show that our proposed framework has more robust and accurate performance compared with state-of-the-art methods. Remarkably, our approach also has the potential to address the problem of link prediction using small fraction of training set.