基于一种变型奇异值分解的有向网络模糊社团提取方法
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摘要
提取复杂网络的社团结构有助于深入分析复杂网络结构特性。本文以模糊分析视角切入有向网络聚类问题,以一种新的矩阵分解方法获取两个具有特定含义的模糊度量,分别对应点到团的有向关联关系和团到点的有向关联关系,可视为对作为模糊聚类结果的点团隶属关系表达方法的一种拓展。在人工生成的有向网络和语义关联网络等网络中验证了算法的可行性和有效性。现实世界中城市路网具有明显方向性,是典型的有向网络,本方法还可为以提高城市路网效能为目的的路网拓扑结构特性研究提供技术手段。
To comprehend the directed networks in a fuzzy view,a new matrix decomposition approach was introduced to extract community structure in weighted and directed networks. This method decomposes a directed network into communites by optimally decomposing the asymmetric feature matrix of the directed network into three matrices separately representing the closeness degree from node to community,the normalized weight matrix and the closeness degree from community to node. By matrix decomposition approach,we obtained a new fuzzy metric characterizing the directed correlation degree between node and community in a directional manner. Their combined result uncovers the community structures in a fuzzy sense in the directed networks. The illustrations on an artificial network and a word association network give reasonable results. This method can also be used to provide researching tools for the study of topological properties of road network.
To comprehend the directed networks in a fuzzy view,a new matrix decomposition approach was introduced to extract community structure in weighted and directed networks. This method decomposes a directed network into communites by optimally decomposing the asymmetric feature matrix of the directed network into three matrices separately representing the closeness degree from node to community,the normalized weight matrix and the closeness degree from community to node. By matrix decomposition approach,we obtained a new fuzzy metric characterizing the directed correlation degree between node and community in a directional manner. Their combined result uncovers the community structures in a fuzzy sense in the directed networks. The illustrations on an artificial network and a word association network give reasonable results. This method can also be used to provide researching tools for the study of topological properties of road network.
引文
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[2]刘铭,闫亚美,黄炎.复杂系统在城市交通网络中的应用[J].科技导报,2017,14(35):27-33.
[3]李建,郑晓艳.复杂网络聚类算法综述[J].电脑知识与技术,2015(5):37-41.
[4]郭玉泉,李雄飞.复杂网络社区的分形聚类检测方法[J].吉林大学学报(工学版),2015(5):1633-1638.
[5]牛艳庆.基于量子模糊聚类算法的复杂网络社团结构探测[J].中南民族大学学报,2015(3):123-125.
[6]曾成,孙雅倩,徐玉珠,等.基于优化的复杂网络聚类方法综述[J].通信技术,2015(8):875-879.
[7]亓慧.基于核心图增量聚类的复杂网络划分算法改进[J].山西大学学报:自然科学版,2015(2):270-275.
[8] Newman M E. Communities,modules and large-scale structure in networks[J]. Nature Physics,2012,8(1):25-31.
[9] Clustering and Community Detection in DirectedNetworks:A Survey[J]. Physics Reports,2013,533(4):95-142.
[10]Jaewon Yang,Julian McAuley,Jure Leskovec.Detecting cohesive and 2-mode communities indirected and undirected networks[C]//AcmInternational Conference on Web Search&DataMining,2014:323-332.
[11]Domenico M D,Lancichinetti A,Arenas A,et al.Identifying modular flows on multilayer networksreveals highly overlapping organization in intercon-nected systems[J]. Physical Review X 5,2015:011027.
[12]J. Yang, J. Leskovec. Overlapping communitydetection at scale:A non-negative factorizationapproach[C]//Proceedings of the sixth ACMinternational conference on Web search and datamining,Rome,Italy,2013:587-596.
[13]Hsieh C J,Dhillon I S. Fast coordinate descentmethods with variable selection for non-negativematrix factorization[C]//Proceedings of the 17thACM SIGKDD international conference onKnowledge discovery and data mining,San Diego,California,USA,2011:1064-1072.
[14]Golub G H,Van Loan C F. Matrix C.omputations[M]. 4rd ed. Baltimore and London:Johns HopkinsUniversity Press,2013:327-329.
[15]Liu Weixiang,Tang Aifa,Ye Datian,et al. Non-negative singular value decomposition for microar-ray data analysis of spermatogenesis[C]//Interna-tional Conference on Information Technology andApplications in Biomedicine,2010:225-228.
[16]Claude S,Geoffrey I. W. Encyclopedia of MachineLearning[M]. 2010 Edition,1201-1242.
[17]肖李明,周玲,张小龙,等.基于PCA谱聚类分析的无功分区方法研究[J].陕西电力,2016(12):23-28.