基于矩阵分解的有向网络交叠团模糊分析与信息挖掘
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摘要
为了逼近真实世界复杂网络,方向性和模糊性是不断发展的网络社团提取方法必须加以考虑的重要特性。在有向网络中研究和分析模糊社团结构具有一定的现实意义。为开发有向网络的模糊社团分析方法,本文构建了一种基于改进的非负奇异值分解法的最优化框架,用矩阵分解技术得到了有向网络中描述点团之间有向关联关系的一种新模糊度量。实验证明新度量不仅能用来提取有向网络的模糊社团,而且可用于对有向网络的社团拓扑结构做深度分析,例如分析社团之间的宏观有向关联关系,对社团间的有向连接贡献程度加以量化并提取重要节点等。城市路网含有大量方向性信息,路网效能强烈依赖其结构鲁棒性,本方法可用于城市路网社团结构划分与脆弱性分析,为提高路网效能提供整体结构特性方面的参考。
It is of practical value to study and analyze the structure of fuzzy communities in directed network. In order to approach the real world complex network,directivity and fuzziness are important characteristics that must be considered in the methods of the network community extraction. To develop fuzzy analysis method in directed network,we introduce an optimal framework of Non-negative Singular Value Decomposition. By matrix decomposition approach,we obtained a new fuzzy metric characterizing the directed correlation degree between node and community in a directional manner. Experiments prove that the new metric can be used not only to extract fuzzy communities in directed networks,but also to analyze the topology of the directed network,such as analysing the directed association between communities or extracting the important nodes. This method can also provide means for the study of topological properties of road network.
It is of practical value to study and analyze the structure of fuzzy communities in directed network. In order to approach the real world complex network,directivity and fuzziness are important characteristics that must be considered in the methods of the network community extraction. To develop fuzzy analysis method in directed network,we introduce an optimal framework of Non-negative Singular Value Decomposition. By matrix decomposition approach,we obtained a new fuzzy metric characterizing the directed correlation degree between node and community in a directional manner. Experiments prove that the new metric can be used not only to extract fuzzy communities in directed networks,but also to analyze the topology of the directed network,such as analysing the directed association between communities or extracting the important nodes. This method can also provide means for the study of topological properties of road network.
引文
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[13]Zhang Z Y,Wang Y,Ahn Y Y. Overlapping com-munity detection in complex networks using sym-metric binary matrix factorization[J]. Physical Re-view,2013,87:062803.
[14]Golub G H,Van Loan C F. Matrix Computations[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,2010:1201-1242.
[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]王俊超,殷志远,冯光柳.复杂网络特性及可靠性分析-以中国航空网为例[J].微型电脑应用,2013,9(11):13-16.
[4]梅丹,王公宝,胡伟文,等.基于复杂网络理论的电力系统脆弱性研究概述[J].电子设计工程,2014(6):190-192.
[5] Rosvall M,Delvenne J-C,Schaub M T,Lambi-otte R. Different approaches to community detection[J]. CoRR,2017,1712:06468.
[6]王兴元,赵仲祥.基于节点间依赖度的社团结构划分方法[J].物理学报,2014,63(17):178901.
[7]骆志刚,丁凡,蒋晓舟,等.复杂网络社团发现算法研究新进展[J].国防科技大学学报,2011,33(1):47-52.
[8] Newman M E. Communities,modules and large-scale structure in networks[J]. Nature Physics,2012,8(1):25-31.
[9] Malliaros F D,Vazirgiannis M. Clustering and com-munity detection in directed networks:A survey[J].Physics Reports,2013(533):95-142.
[10]Alex A,Javier B-H,Sergio G,et al. Optimal mapof the modular structure of complex networks[J].New Journal of Physics,2010(12):053009.
[11]Xie J,Kelley S,Szymanski B K. Overlapping com-munity detection in networks:The state-of-the-artand comparative study[J]. ACM Computing Surveys(CSUR),2013,45(4):43-79.
[12]付立东.非负矩阵分解的复杂网络社团检测方法[J].计算机工程与设计,2010,31(11):2449-2451.
[13]Zhang Z Y,Wang Y,Ahn Y Y. Overlapping com-munity detection in complex networks using sym-metric binary matrix factorization[J]. Physical Re-view,2013,87:062803.
[14]Golub G H,Van Loan C F. Matrix Computations[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,2010:1201-1242.
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