Quantifying multiple social relationships based on a multiplex stochastic block model

Abstract

Online social networks have attracted great attention recently, because they make it easy to build social connections for people all over the world. However, the observed structure of an online social network is always the aggregation of multiple social relationships. Thus, it is of great importance for real-world networks to reconstruct the full network structure using limited observations. The multiplex stochastic block model is introduced to describe multiple social ties, where different layers correspond to different attributes (e.g., age and gender of users in a social network). In this letter, we aim to improve the model precision using maximum likelihood estimation, where the precision is defined by the cross entropy of parameters between the data and model. Within this framework, the layers and partitions of nodes in a multiplex network are determined by natural node annotations, and the aggregate of the multiplex network is available. Because the original multiplex network has a high degree of freedom, we add an independent functional layer to cover it, and theoretically provide the optimal block number of the added layer. Empirical results verify the effectiveness of the proposed method using four measures, i.e., error of link probability, cross entropy, area under the receiver operating characteristic curve, and Bayes factor.

摘要

在线社交网络使世界各地的人们能够方便地建立各种社交关系, 受到极大关注. 但是, 观测到的社交网络结构往往是多种社交关系的聚合结构. 因此, 通过观测到的单层结构完整地重构真实网络的多重结构非常重要. 本文通过多层网络随机块模型描述多重社交关系, 其中不同层对应不同属性 (例如, 社交网络用户的年龄和性别). 本文旨在利用最大似然估计提高模型参数估计精度, 其中估计精度由数据和模型参数之间的交叉熵定义. 在本文中, 多重网络中每一层节点的分类由其自然属性决定, 并且假设多重网络的单层聚合结构已知. 由于原多重网络具有较高自由度, 因此通过添加一个独立的功能层增加模型参数, 以充分覆盖自由度, 并在理论上获得功能层的最佳分块数. 最后, 通过仿真实验, 从链接概率误差、 交叉熵、 接收者操作特征曲线以及贝叶斯因子4个角度验证了本文方法的有效性.