Importance of the topic Girvan M Newman M
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Importance of the topic Girvan, M, Newman, M. , 7 Proc. Natl. Acad. Sci, 2002 Ravasz, E, Somera, A, Mongru, D, Oltvai, Z, Barabasi, A. , Science, 2002 Radicchi, F, Castellano, C, Cecconi, F. , Proc. Natl. Acad. Sci, 2004 Guimera, R, Mossa, S, Turtschi, A. , Proc. Natl. Acad. Sci, 2005 Guimera, R, Amaral, L. , Nature, 2005 Newman, M. , Proc. Natl. Acad. Sci, 2006 Rosvall, M, Bergstrom, C. , Proc. Natl. Acad. Sci, 2007 Fortunato, S, Barthelemy, M. , Proc. Natl. Acad. Sci, 2007 生物信息学与最优化方法 Weinan, E, Li, T, Vanden-Eijnden, E. , Proc. Natl. Acad. Sci,
社团结构探索方法概述 A large number of methods have been developed for detecting communities, which can be generally categorized into local and global methods. Local methods for community detection identify a subset of nodes as a community according to certain local connection conditions, independently from the structure of the rest of the network. Such methods include clique overlap-based hierarchical clustering, clique percolation method, and sub-graph fitness method. Global methods for community detection optimize certain global quantitative functions encoding the quality of the overall partition of the network, such as information theoretical method, Potts model, and optimization of modularity measures. 8
l我们小组在研究这一问题的早期发展了一些基于图论和 矩阵谱分解的模块探测算法 (local method) Shihua Zhang, Rui-Sheng Wang, and Xiang-Sun Zhang. Identification of overlapping community structure in complex networks using fuzzy cmeans Clustering. Physica A, 2007, 374, 483– 490. Shihua Zhang, Rui-Sheng Wang and Xiang-Sun Zhang. Uncovering fuzzy community structure in complex networks. Physical Review E, 76, 046103, 2007 Rui-Sheng Wang, Shihua Zhang, Yong Wang, Xiang-Sun Zhang, Luonan Chen. Clustering complex networks and biological networks by nonnegative matrix factorization with various similarity measures. Neurocomputing, 2007 9
极端例子:ring of cliques Fortunato & Barthelemy, Proc. Natl. Acad. Sci. USA 104 (1), 36 -41 (2007) 12
提出新的模块化指标D值 模块化密度函数 D: Zhenping Li, Shihua Zhang, Rui-Sheng Wang, Xiang-Sun Zhang, Luonan Chen, Quantitative function for community detection. Physical Review E, 77, 036109, 2008 13
D值克服了Q值存在的 resolution limit 问题 14
错分现象---Misidentification 用Q或D作优化可能得到不满足定义的模块 Q partitions the network into three communities (two Kn and one K 5) when n>=16 (respectively, n>=21), in which K 5 is a sub-graph violating all reasonable community definition. Xiang-Sun Zhang, Rui-Sheng Wang, Yong Wang, Ji-Guang Wang, Yu-Qing Qiu, Lin Wang, and Luonan Chen. Modularity optimization in community detection of complex networks. Europhysics Letters (EPL), 87, 2009. 被评为 EPL 2009 best paper 16
Finding 1 对
为了彻底解决这些问题 提出一个新的 OR 模型和相应的算法,这一算法不会产生 resolution limit 和 mis-identification 现象 Xiang-Sun Zhang, Zhenping Li, Rui-Sheng Wang, Yong Wang. A combinatorial model and algorithm for globally searching community structure in complex networks Journal of Combinatorial Optimization (JCO), 2010. DOI: 10. 1007/s 10878 -010 -9356 -0 23
A new OR model Problem definition: Given a network, the community identification problem is to partition the network into as many non-overlapping sub-networks as possible such that each sub-network satisfies a given community definition. 24
A qualified min-cut (QMC) algorithm A heuristic principle is given to find a feasible partition with the largest number of communities. It is realized by a min-cut operation: A min- cut operation is called qualified if the two resulting sub-networks satisfy the module definition. The community identification problem can be 26 solved based on a series of qualified min-cut operations.
Experiment results (artificial networks) Rings of cliques 27 Uneven ad-hoc network
Experiment results (real networks) Football team network 28 Jazz musician network
致谢 This work is cooperated with Dr. 李珍萍,Dr. 王瑞省,Dr. 王勇,Dr. 张世华, Dr. 王吉光,Dr. 张俊华 This work is supported by 国家自然科学重点基金 10631070 973项目 2066 CB 503905 国家自然科学基金项目 60873205 29
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