Abstract: Community detection has been one of the key research directions in network analysis. Most of the current network community detection algorithms mainly use the structural information of the network to adopt a greedy algorithm to maximize a certain indicator, which cannot fully consider the node feature information, edge weight, and network community relationship asymmetry. To address this situation, this paper proposes an autoencoder-like modularity nonnegative matrix factorization (AMNMF) community detection algorithm. The algorithm expands the depth of non-negative matrix factorization by using an encoder-like structure, and introduces modularity and graph regularizer into the objective function optimization process of non-negative matrix factorization to fully mine the node and community structure information in the network. The problem of community relationship imbalance is solved by adding orthogonal constraints to the middle layer of the encoder. Experiments on multiple real networks show that：AMNMF is an effective NMF extension algorithm that uses node feature information and network structure information. Compared with the best results of baseline algorithms, it achieves an improvement of about 15% to 122%, and can accurately and effectively complete the community detection task.

Key words: nonnegative matrix decomposition, community testing, autoencoding, modular

摘要： 社区检测一直是网络分析中的重点研究方向之一。目前大多数网络社区检测算法主要利用网络的结构信息采用贪心算法使某一指标最大化，无法充分考虑节点特征信息、边权重以及网络社区间关系不对称性等问题。针对这一情况，提出一种自编码模块化增强非负矩阵分解（autoencoder-like modularity nonnegative matrix factorization，AMNMF）社区检测算法。该算法通过采用类编码器结构拓展非负矩阵分解的深度，将模块度和图正则化器引入到非负矩阵分解的目标函数优化过程中以充分挖掘网络中的节点和社区结构信息，通过在编码器中间层添加正交约束解决了社区间关系不平衡的问题。在多个真实网络上的实验表明：AMNMF是一种有效地利用节点特征信息和网络结构信息的NMF拓展算法，与基线算法的最佳结果相比实现了约15%至122%的提升，能够准确有效完成社区检测任务。

关键词: 非负矩阵分解, 社区检测, 自编码, 模块化