In this article, we develop a clique-based method for social network clustering. We introduce a new index to evaluate the quality of clustering results, and propose an efficient algorithm based on recursive bipartition to maximize an objective function of the proposed index. The optimization problem is NP-hard, so we approximate the semi-optimal solution via an implicitly restarted Lanczos method. One of the advantages of our algorithm is that the proposed index of each community in the clustering result is guaranteed to be higher than some predetermined threshold, p , which is completely controlled by users. We also account for the situation that p is unknown. A statistical procedure of controlling both under-clustering and over-clustering errors simultaneously is carried out to select localized threshold for each subnetwork, such that the community detection accuracy is optimized. Accordingly, we propose a localized clustering algorithm based on binary tree structure. Finally, we exploit the stochastic blockmodels to conduct simulation studies and demonstrate the accuracy and efficiency of our algorithms, both numerically and graphically.

中文翻译：

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基于群的社交网络聚类方法

在本文中，我们开发了一种基于集团的社交网络聚类方法。我们引入了一个新的指标来评估聚类结果的质量，并提出了一种基于递归二分法的有效算法来最大化所提出指标的目标函数。优化问题是 NP-hard，因此我们通过隐式重新启动的 Lanczos 方法来近似半最优解。我们算法的优点之一是，聚类结果中每个社区的建议索引保证高于某个预先确定的阈值 p ，该阈值完全由用户控制。我们还考虑了 p 未知的情况。执行同时控制欠聚类和过聚类错误的统计过程，以选择每个子网的局部阈值，从而优化社区检测的准确性。因此，我们提出了一种基于二叉树结构的局部聚类算法。最后，我们利用随机块模型进行模拟研究，并以数值和图形方式证明我们算法的准确性和效率。