Link predication based on matrix factorization by fusion of multi class organizations of the network

Link predication aims at forecasting the latent or unobserved edges in the complex networks and has a wide range of applications in reality. Almost existing methods and models only take advantage of one class organization of the networks, which always lose important information hidden in other organizations of the network. In this paper, we propose a link predication framework which makes the best of the structure of networks in different level of organizations based on nonnegative matrix factorization, which is called NMF ³ here. We first map the observed network into another space by kernel functions, which could get the different order organizations. Then we combine the adjacency matrix of the network with one of other organizations, which makes us obtain the objective function of our framework for link predication based on the nonnegative matrix factorization. Third, we derive an iterative algorithm to optimize the objective function, which converges to a local optimum, and we propose a fast optimization strategy for large networks. Lastly, we test the proposed framework based on two kernel functions on a series of real world networks under different sizes of training set, and the experimental results show the feasibility, effectiveness, and competitiveness of the proposed framework.