Community is a fundamental and critical characteristic of an undirected social network, making community detection be a vital yet thorny issue in network representation learning. A symmetric and non-negative matrix factorization (SNMF) model is frequently adopted to address this issue owing to its great interpretability and scalability. However, it adopts a single latent factor matrix to represent an undirected network for precisely representing its symmetry, which leads to loss of representation learning ability due to the reduced latent space. Motivated by this discovery, this paper proposes a novel Constraints Fusion-induced Symmetric Nonnegative Matrix Factorization (CFS) model that adopts three-fold ideas: a) Representing a target undirected network with multiple latent factor matrices, thus preserving its representation learning capacity; b) Incorporating a symmetry-regularizer that preserves the symmetry of the learnt low-rank approximation to the adjacency matrix into the loss function, thus making the resultant detector well-aware of the target network's symmetry; and c) Introducing a graph-regularizer that preserves local invariance of the network's intrinsic geometry, thus making the achieved detector well-aware of community structure within the target network. Extensively empirical studies on eight real-world social networks from industrial applications demonstrate that the proposed CFS model significantly outperforms state-of-the-art models in achieving highly-accurate community detection results.

翻译：社区是无向社会网络的基本且关键特征，使得社区检测成为网络表示学习中重要且棘手的难题。对称非负矩阵分解（SNMF）模型因其良好的可解释性和可扩展性常被用于解决该问题。然而，该模型采用单一潜在因子矩阵表示无向网络以精确保持其对称性，这因潜在空间缩减而导致表示学习能力下降。基于此发现，本文提出一种新颖的约束融合诱导的对称非负矩阵分解（CFS）模型，其采用三重思路：a) 用多个潜在因子矩阵表示目标无向网络，从而保留其表示学习能力；b) 在损失函数中引入对称正则化项，保持学习到的邻接矩阵低秩近似的对称性，使所得检测器充分感知目标网络的对称性；c) 引入图正则化项，保持网络内在几何结构的局部不变性，使所得检测器充分感知目标网络内的社区结构。在来自工业应用的八个真实世界社交网络上进行的广泛实证研究表明，所提出的CFS模型在实现高精度社区检测结果方面显著优于现有最优模型。