Incorporating affiliation preference into overlapping community detection

Community detection is an important way to understand structures of complex networks. Many conventional methods assume that each node only belongs to one community. However, nodes may have multiple memberships in real-world networks. Recently, overlapping community detection has attracted lots of attention. With the good interpretability of latent vectors, in this paper, we improve non-negative matrix factorization method by incorporating affiliation preference. Other than directly approximating original adjacent matrix of network, our proposed Bayesian Affiliation Preference based Non-negative Matrix Factorization (BAPNMF) method maximizes the likelihood of affiliation preferences for all nodes. The intuition is that nodes prefer their neighbors than non-neighbors. We define the edge preference possibility which satisfies the totality based on generative affiliation model. In the learning phase, stochastic gradient descent with bootstrap sampling is adopted. We evaluated on both synthetic and real-world networks, and results show our method outperforms state-of-art algorithms and is scalable for large-scale networks.