Abstract

Community detection in network data aims at grouping similar nodes sharing certain characteristics together. Most existing methods focus on detecting communities in undirected networks, where similarity between nodes is measured by their node features and whether they are connected. In this article, we propose a novel method to conduct network embedding and community detection simultaneously in a directed network. The network embedding model introduces two sets of vectors to represent the out- and in-nodes separately, and thus allows the same nodes belong to different out- and in-communities. The community detection formulation equips the negative log-likelihood with a novel regularization term to encourage community structure among the nodes representations, and thus achieves better performance by jointly estimating the nodes embeddings and their community structures. To tackle the resultant optimization task, an efficient alternative updating scheme is developed. More importantly, the asymptotic properties of the proposed method are established in terms of both network embedding and community detection, which are also supported by numerical experiments on some simulated and real examples.

摘要

网络数据中的社区检测旨在将共享某些特征的相似节点分组在一起。大多数现有方法侧重于检测无向网络中的社区，其中节点之间的相似性通过其节点特征以及它们是否连接来衡量。在本文中，我们提出了一种在有向网络中同时进行网络嵌入和社区检测的新方法。网络嵌入模型引入两组向量分别表示出节点和入节点，从而允许相同的节点属于不同的出社区和入社区。社区检测公式为负对数似然配备了一个新的正则化项，以鼓励节点表示之间的社区结构，从而通过联合估计节点嵌入及其社区结构来获得更好的性能。为了解决由此产生的优化任务，开发了一种有效的替代更新方案。更重要的是，所提出方法的渐近特性是在网络嵌入和社区检测方面建立的，这也得到了一些模拟和真实例子的数值实验的支持。