ABSTRACT

Networks are widely used to describe relational data among objects in a complex system. As network data often exhibit clustering structures, research interest often focuses on discovering clusters of nodes. We develop a novel concordance-based method for node clustering in networks, where a linear model is imposed on the latent position of each node with respect to a node-specific center and its covariates via linear transformation. By maximizing a triangular concordance function with a concave pairwise penalty, the latent positions are estimated so that each node would be more likely to be close to its neighbors in contrast to non-neighbors and nodes are clustered by their node-specific centers. We develop an alternating direction method of multipliers algorithm for parameter estimation and an intimacy score between unlinked nodes for link prediction. Our method takes into account common characteristics of network data (i.e., assortativity, link pattern similarity, node heterogeneity and link transitivity), while it does not require the number of clusters to be known. The clustering effectiveness and link prediction accuracy of our method are demonstrated in simulated and real networks. Supplementary materials for this article are available online.

摘要

网络广泛用于描述复杂系统中对象之间的关系数据。由于网络数据通常表现出聚类结构，因此研究兴趣通常集中在发现节点聚类上。我们开发了一种新颖的基于一致性的网络中节点聚类方法，其中通过线性变换将线性模型强加于每个节点相对于特定节点中心及其协变量的潜在位置。通过使用凹成对惩罚来最大化三角一致性函数，估计潜在位置，使得每个节点与非邻居相比更有可能靠近其邻居，并且节点通过其特定于节点的中心进行聚类。我们开发了用于参数估计的乘数算法的交替方向方法和用于链接预测的未链接节点之间的亲密度分数。我们的方法考虑了网络数据的共同特征（即相配性、链接模式相似性、节点异质性和链接传递性），同时不需要知道簇的数量。我们的方法的聚类有效性和链接预测准确性在模拟和真实网络中得到了证明。本文的补充材料可在线获取。我们的方法的聚类有效性和链接预测准确性在模拟和真实网络中得到了证明。本文的补充材料可在线获取。我们的方法的聚类有效性和链接预测准确性在模拟和真实网络中得到了证明。本文的补充材料可在线获取。