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.

社区检测是了解复杂网络结构的重要方法。许多常规方法假定每个节点仅属于一个社区。但是，在现实网络中，节点可能具有多个成员资格。最近，重叠的社区检测引起了很多关注。借助潜在向量的良好解释性，本文通过结合隶属关系偏好来改进非负矩阵分解方法。除了直接逼近网络的原始相邻矩阵外，我们提出的基于贝叶斯联系偏好的非负矩阵分解（BAPNMF）方法最大程度地提高了所有节点的联系偏好的可能性。直觉是，节点比非邻居更喜欢它们的邻居。我们基于生成隶属关系模型定义满足总体需求的边缘偏好可能性。在学习阶段，采用具有自举抽样的随机梯度下降法。我们在综合网络和实际网络上进行了评估，结果表明我们的方法优于最新算法，并且可扩展到大规模网络。