The real-world complex networks, such as biological, transportation, biomedical, web, and social networks, are usually dynamic and change over time. The communities which reflect the substructures hidden in the networks usually overlap each other, and detecting overlapping communities in the dynamic complex networks is a challenging task. Prior researchers have applied multiobjective optimization method to the detection of dynamic overlapping communities and achieved some excellent results. However, in terms of multiobjective processing, the prior studies all adopt the decomposition method based on weight parameters, and different weight parameters or different parameter values can easily affect the community detection results which further results in the uneven distribution of the detected results in the target space. To solve the above problems, a hybrid algorithm, that is, Collaborative Particle Swarm multiobjective Optimization-based Dynamic Overlapping Community Detection (CPSO-DOCD) algorithm is proposed in this paper. First, to improve the diversity of particles, the encoding/decoding of the particle and the cross inheritance and the variation of particle are redefined first based on label propagation. In each network snapshot, multiple particle swarms are initialized based on Community Overlap Propagation Algorithm (COPRA) to generate particles with uniform distribution. Multiple different objective functions are optimized using multiple particle swarms respectively to avoid the incorrect selection of weight parameters. In addition, a reference-point-based is adopted in the particle selecting stage to solve the uneven distribution of detected results in the target space. Second, a node label entropy-based particle swarm algorithm is proposed to improve the accuracy of community detection of current network snapshots. Finally, when one snapshot switches to another over time, a migration strategy based on COPRA local-search and clique generation is utilized to adjust the prior community detection results, which enables the former results can be adapted to the new network snapshots. The experiments are implemented based on four dynamic networks which are Cit-HepPh, Cit-HepTh, Emailed-EU-core-temporal, and CollegeMsg. The hypervolume value of the overlapping community detection result obtained by CPSO-DOCD is 0.5%–2% higher than MDOA, MCMOEA, SLPAD, and iLCD. Furthermore, CPSO-DOCD also performed better than MDOA, MCMOEA, SLPAD, and iLCD on C-metric values, and CPSO-DOCD can approach approximately to the Pareto frontier.

中文翻译：

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复杂网络中动态重叠社区检测的基于标签熵的协同粒子群优化算法

现实世界的复杂网络，例如生物、交通、生物医学、网络和社交网络，通常是动态的，并且会随着时间而变化。反映隐藏在网络中的子结构的社区通常相互重叠，在动态复杂网络中检测重叠社区是一项具有挑战性的任务。之前的研究人员已经将多目标优化方法应用于动态重叠社区的检测，并取得了一些优异的成果。然而，在多目标处理方面，以往的研究都采用基于权重参数的分解方法，不同的权重参数或不同的参数值很容易影响社区检测结果，进而导致检测结果在目标中的分布不均。空间。为解决以上问题，本文提出了一种混合算法，即基于协同粒子群多目标优化的动态重叠社区检测(CPSO-DOCD)算法。首先，为了提高粒子的多样性，首先基于标签传播重新定义粒子的编码/解码以及粒子的交叉继承和变异。在每个网络快照中，基于社区重叠传播算法（COPRA）初始化多个粒子群以生成分布均匀的粒子。多个不同的目标函数分别使用多个粒子群进行优化，以避免权重参数的错误选择。此外，在粒子选择阶段采用了基于参考点的方法来解决目标空间中检测结果分布不均的问题。第二，提出了一种基于节点标签熵的粒子群算法，以提高当前网络快照社区检测的准确性。最后，当一个快照随着时间的推移切换到另一个快照时，利用基于 COPRA 本地搜索和派系生成的迁移策略来调整先前的社区检测结果，使之前的结果可以适应新的网络快照。实验基于 Cit-HepPh、Cit-HepTh、Emailed-EU-core-temporal 和 CollegeMsg 四个动态网络实现。CPSO-DOCD 获得的重叠社区检测结果的 hypervolume 值比 MDOA、MCMOEA、SLPAD 和 iLCD 高 0.5%–2%。此外，CPSO-DOCD 的表现也优于 MDOA、MCMOEA、SLPAD 和 iLCD 当一个快照随着时间的推移切换到另一个快照时，基于 COPRA 本地搜索和派系生成的迁移策略被用来调整先前的社区检测结果，使之前的结果可以适应新的网络快照。实验基于 Cit-HepPh、Cit-HepTh、Emailed-EU-core-temporal 和 CollegeMsg 四个动态网络实现。CPSO-DOCD 获得的重叠社区检测结果的 hypervolume 值比 MDOA、MCMOEA、SLPAD 和 iLCD 高 0.5%–2%。此外，CPSO-DOCD 的表现也优于 MDOA、MCMOEA、SLPAD 和 iLCD 当一个快照随着时间的推移切换到另一个快照时，基于 COPRA 本地搜索和派系生成的迁移策略被用来调整先前的社区检测结果，使之前的结果可以适应新的网络快照。实验基于 Cit-HepPh、Cit-HepTh、Emailed-EU-core-temporal 和 CollegeMsg 四个动态网络实现。CPSO-DOCD 获得的重叠社区检测结果的 hypervolume 值比 MDOA、MCMOEA、SLPAD 和 iLCD 高 0.5%–2%。此外，CPSO-DOCD 的表现也优于 MDOA、MCMOEA、SLPAD 和 iLCD 这使得以前的结果可以适应新的网络快照。实验基于 Cit-HepPh、Cit-HepTh、Emailed-EU-core-temporal 和 CollegeMsg 四个动态网络实现。CPSO-DOCD 获得的重叠社区检测结果的 hypervolume 值比 MDOA、MCMOEA、SLPAD 和 iLCD 高 0.5%–2%。此外，CPSO-DOCD 的表现也优于 MDOA、MCMOEA、SLPAD 和 iLCD 这使得以前的结果可以适应新的网络快照。实验基于 Cit-HepPh、Cit-HepTh、Emailed-EU-core-temporal 和 CollegeMsg 四个动态网络实现。CPSO-DOCD 获得的重叠社区检测结果的 hypervolume 值比 MDOA、MCMOEA、SLPAD 和 iLCD 高 0.5%–2%。此外，CPSO-DOCD 的表现也优于 MDOA、MCMOEA、SLPAD 和 iLCDC 度量值和 CPSO-DOCD 可以近似接近帕累托边界。