论文标题
稀疏网络上的协变量社区检测
Covariate-Assisted Community Detection on Sparse Networks
论文作者
论文摘要
处理网络数据时，社区检测是一个重要的问题。传统上，这是通过利用节点之间的连接来完成的，但是连接可能太少了，无法检测许多实际数据集中的社区。节点协变量可用于协助社区检测；参见Binkiewicz等。 （2017）; Weng and Feng（2022）; Yan and Sarkar（2021）；杨等。 （2013）。但是，如何将协变量与网络连接相结合是具有挑战性的，因为协变量可能是高维且与社区标签不一致的。为了研究协变量与社区之间的关系，我们提出了用节点协变量（DCSBM-NC）校正了随机块模型。它允许社区之间的学位异质性以及社区和协变量之间的标签不一致。基于DCSBM-NC，我们设计了调整后的邻居辅助（ANC）数据矩阵，该数据矩阵利用协变量信息来帮助社区检测。然后，我们提出了协变量辅助光谱群集在ANC矩阵上的单数矢量（CA得分）方法的比率上。我们证明，当1）网络相对密集时，CA得分成功恢复了社区标签； 2）协变班级标签与社区标签相匹配； 3）数据是1）和2）的混合物。 CA得分在合成和真实数据集上具有良好的性能。该算法在R（R Core Team（2021））软件包cascore中实现。
Community detection is an important problem when processing network data. Traditionally, this is done by exploiting the connections between nodes, but connections can be too sparse to detect communities in many real datasets. Node covariates can be used to assist community detection; see Binkiewicz et al. (2017); Weng and Feng (2022); Yan and Sarkar (2021); Yang et al. (2013). However, how to combine covariates with network connections is challenging, because covariates may be high-dimensional and inconsistent with community labels. To study the relationship between covariates and communities, we propose the degree corrected stochastic block model with node covariates (DCSBM-NC). It allows degree heterogeneity among communities and inconsistent labels between communities and covariates. Based on DCSBM-NC, we design the adjusted neighbor-covariate (ANC) data matrix, which leverages covariate information to assist community detection. We then propose the covariate-assisted spectral clustering on ratios of singular vectors (CA-SCORE) method on the ANC matrix. We prove that CA-SCORE successfully recovers community labels when 1) the network is relatively dense; 2) the covariate class labels match the community labels; 3) the data is a mixture of 1) and 2). CA-SCORE has good performance on synthetic and real datasets. The algorithm is implemented in the R(R Core Team (2021)) package CASCORE.
