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.

在线社交网络最近引起了极大的关注，因为它们使与全世界的人们建立社交联系变得容易。但是，观察到的在线社交网络结构始终是多个社交关系的集合。因此，对于现实世界的网络而言，使用有限的观察来重建完整的网络结构非常重要。引入了多元随机块模型来描述多个社会纽带，其中不同的层对应于不同的属性（例如，社交网络中用户的年龄和性别）。在这封信中，我们旨在使用最大似然估计来提高模型精度，其中精度由数据和模型之间的参数交叉熵定义。在这个框架内，多路复用网络中节点的层和分区由自然节点注释确定，并且多路复用网络的聚合可用。由于原始的多路复用网络具有很高的自由度，因此我们添加了一个独立的功能层来覆盖它，并在理论上提供了添加层的最佳块数。经验结果使用四种测量方法验证了所提方法的有效性，即链路概率误差，交叉熵，接收机工作特性曲线下的面积以及贝叶斯因子。