From Mutual Friends to Overlapping Community Detection: A Non-negative Matrix Factorization Approach.

Community detection provides a way to unravel complicated structures in complex networks. Overlapping community detection allows nodes to be associated with multiple communities. Matrix Factorization (MF) is one of the standard tools to solve overlapping community detection problems from a global view. Existing MF-based methods only exploit link information revealed by the adjacency matrix, but ignore other critical information. In fact, compared with the existence of a link, the number of mutual friends between two nodes can better reflect their similarity regarding community membership. In this paper, based on the concept of mutual friend, we incorporate Mutual Density as a new indicator to infer the similarity of community membership between two nodes in the MF framework for overlapping community detection. We conduct data observation on real-world networks with ground-truth communities to validate an intuition that mutual density between two nodes is correlated with their community membership cosine similarity. According to this observation, we propose a Mutual Density based Non-negative Matrix Factorization (MD-NMF) model by maximizing the likelihood that node pairs with larger mutual density are more similar in community memberships. Our model employs stochastic gradient descent with sampling as the learning algorithm. We conduct experiments on various real-world networks and compare our model with other baseline methods. The results show that our MD-NMF model outperforms the other state-of-the-art models on multiple metrics in these benchmark datasets.