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Constrained common cluster based model for community detection in temporal and multiplex networks

机译：基于约束通用簇的时间和多路复用网络社区检测模型

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摘要

On one hand, the detection of tightly connected groups, also known as community detection in complex networks, is a prominent problem for network analysis and mining. On the other hand, almost all of social, biological, bibliographic, communication and computer systems are modeled as temporal networks, the topological structures of which evolve with time, or multiplex networks, each pair of nodes of which has multiple linked relations. Current methods of community detection for temporal networks are based on incremental, independent or evolutionary clustering, and for multiplex networks are based on fusion of the multiple links. However, all these methods ignore the common structure hidden in the networks, which is denoted as the common cluster here. So in this paper, we propose a constrained common cluster based model (C-3 model) to analyze the temporal and multiplex networks, which can not only detect the community structure, but also identify the importance of each node based on the common cluster structure of both two classes of networks. The intrinsic assumption of the proposed model is that there are common or coincident clusters hidden in these networks. In detail, we first construct the Markov steady-state matrices of each snapshot of temporal network or each slice of multiplex network. Next, we propose the object function of C-3 model by combining the Markov steady-state matrices, similarity matrices with community membership matrices of each snapshot or slice of the network. Last, a gradient descent algorithm based on non-negative matrix factorization is proposed for the object function. Experiments on both synthetic datasets and real-world networks demonstrate that the proposed C-3 model has competitive performance based on the evaluation indexes NMI and error of community detection, otherwise, the proposed model could identify the importance of nodes of the temporal or multiplex networks. (c) 2017 Elsevier B.V. All rights reserved.
机译：一方面，紧密连接的组的检测（也称为复杂网络中的社区检测）是网络分析和挖掘的突出问题。另一方面，几乎所有的社会，生物学，书目，通信和计算机系统都被建模为时间网络，其拓扑结构随时间而发展，或者是多路复用网络，其每对节点都具有多个链接关系。当前的时间网络社区检测方法基于增量，独立或进化聚类，而多路复用网络则基于多个链接的融合。但是，所有这些方法都忽略了隐藏在网络中的公共结构，此处将其称为公共群集。因此，在本文中，我们提出了一种基于约束的通用集群模型（C-3模型）来分析时间网络和多路复用网络，该模型不仅可以检测社区结构，而且可以基于通用集群结构确定每个节点的重要性这两类网络所提出模型的内在假设是这些网络中隐藏着公共或重合的集群。详细地，我们首先构造时间网络的每个快照或复用网络的每个切片的马尔可夫稳态矩阵。接下来，我们通过将Markov稳态矩阵，相似性矩阵与网络的每个快照或切片的社区成员资格矩阵相结合，提出C-3模型的目标函数。最后，针对目标函数提出了一种基于非负矩阵分解的梯度下降算法。在合成数据集和真实世界网络上进行的实验表明，基于评估指标NMI和社区检测错误，所提出的C-3模型具有竞争性，否则，该模型可以识别时间网络或多路复用网络节点的重要性。 （c）2017 Elsevier B.V.保留所有权利。

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