The community plays a crucial role in understanding user behavior and network
characteristics in social networks. Some users can use multiple social networks
at once for a variety of objectives. These users are called overlapping users
who bridge different social networks. Detecting communities across multiple
social networks is vital for interaction mining, information diffusion, and
behavior migration analysis among networks. This paper presents a community
detection method based on nonnegative matrix tri-factorization for multiple
heterogeneous social networks, which formulates a common consensus matrix to
represent the global fused community. Specifically, the proposed method
involves creating adjacency matrices based on network structure and content
similarity, followed by alignment matrices which distinguish overlapping users
in different social networks. With the generated alignment matrices, the method
could enhance the fusion degree of the global community by detecting
overlapping user communities across networks. The effectiveness of the proposed
method is evaluated with new metrics on Twitter, Instagram, and Tumblr
datasets. The results of the experiments demonstrate its superior performance
in terms of community quality and community fusion.

提出一种基于非负矩阵三因子分解的社区检测方法，用于多个异构社交网络，通过检测不同社交网络中的重叠用户社区来增强全局社区的融合程度，并在 Twitter、Instagram 和 Tumblr 数据集上展示其卓越的社区质量和社区融合性能。

异构多社交网络的社区检测

Community Detection for Heterogeneous Multiple Social Networks

Conventional fair graph clustering methods face two primary challenges: i)
They prioritize balanced clusters at the expense of cluster cohesion by
imposing rigid constraints, ii) Existing methods of both individual and
group-level fairness in graph partitioning mostly rely on eigen decompositions
and thus, generally lack interpretability. To address these issues, we propose
iFairNMTF, an individual Fairness Nonnegative Matrix Tri-Factorization model
with contrastive fairness regularization that achieves balanced and cohesive
clusters. By introducing fairness regularization, our model allows for
customizable accuracy-fairness trade-offs, thereby enhancing user autonomy
without compromising the interpretability provided by nonnegative matrix
tri-factorization. Experimental evaluations on real and synthetic datasets
demonstrate the superior flexibility of iFairNMTF in achieving fairness and
clustering performance.

通过引入公平性正则化，提出了一种个体公平性非负矩阵三因子分解模型（iFairNMTF），该模型能够在平衡和连贯的聚类中实现可定制的准确性 - 公平性权衡，同时提供非负矩阵三因子分解的可解释性，从而增强用户自主性，并在真实和合成数据集上展示了 iFairNMTF 在实现公平性和聚类性能方面的优越灵活性。