A novel evolutionary clustering via the first-order varying information for dynamic networks

Abstract Temporal community detection could help us analyze and understand the meaningful substructure hidden within dynamic networks in the real world. Evolutionary clustering, as a popular framework for clustering stream data, has been denoted for mining the communities in dynamic networks. However, most of these methods ignore the varying characteristics of micro structure of the networks and lack of statistical interpretation. In this paper, we propose a powerful, interpretable and extensible evolutionary clustering framework based on nonnegative matrix factorization (NMF) for temporal community detection via combining the first-order varying information of micro structure in dynamic networks from the perspective of statistical model. Firstly, we consider the first-order varying information of nodes by constructing a temporal similarity matrix over time. Secondly, we present the framework, FVI-NMF, for detecting temporal community based on NMF combining the First-order Varying Information. Thirdly, we develop a effective algorithm to optimize the objective function of FVI-NMF and analyze its complexity. In addition, our model can discover the evolutionary pattern of temporal communities synchronously, which has a variety applications in the analysis of dynamic network. Experiments on both artificial and real dynamic networks demonstrate that our proposed framework has superior performance in comparison with state-of-art methods.

[1]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[2]  Leon Danon,et al.  Comparing community structure identification , 2005, cond-mat/0505245.

[3]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[4]  Derek Greene,et al.  Tracking the Evolution of Communities in Dynamic Social Networks , 2010, 2010 International Conference on Advances in Social Networks Analysis and Mining.

[5]  Xiaochun Cao,et al.  Exploring the roles of cannot-link constraint in community detection via Multi-variance Mixed Gaussian Generative Model , 2017, PloS one.

[6]  Yun Chi,et al.  Analyzing communities and their evolutions in dynamic social networks , 2009, TKDD.

[7]  Santo Fortunato,et al.  A benchmark model to assess community structure in evolving networks , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Jiawei Han,et al.  A Particle-and-Density Based Evolutionary Clustering Method for Dynamic Networks , 2009, Proc. VLDB Endow..

[9]  Yunming Ye,et al.  Clustering time-stamped data using multiple nonnegative matrices factorization , 2016, Knowl. Based Syst..

[10]  Dongmei Ye,et al.  A Distance-Based Spectral Clustering Approach with Applications to Network Community Detection , 2017, ISPE TE.

[11]  Charu C. Aggarwal,et al.  Evolutionary Network Analysis , 2014, ACM Comput. Surv..

[12]  Fei Wang,et al.  Community discovery using nonnegative matrix factorization , 2011, Data Mining and Knowledge Discovery.

[13]  Dongxiao He,et al.  Autonomous overlapping community detection in temporal networks: A dynamic Bayesian nonnegative matrix factorization approach , 2016, Knowl. Based Syst..

[14]  Dong Liu,et al.  Semi-supervised community detection based on discrete potential theory , 2014 .

[15]  Prakash Ishwar,et al.  Node Embedding via Word Embedding for Network Community Discovery , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[16]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[17]  Yihong Gong,et al.  Detecting communities and their evolutions in dynamic social networks—a Bayesian approach , 2011, Machine Learning.

[18]  Philip S. Yu,et al.  GraphScope: parameter-free mining of large time-evolving graphs , 2007, KDD '07.

[19]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.

[20]  Mark E. J. Newman.  A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[21]  Giulio Rossetti,et al.  Community Discovery in Dynamic Networks , 2017, ACM Comput. Surv..

[22]  Yuguo Chen,et al.  Latent Space Approaches to Community Detection in Dynamic Networks , 2017, 2005.08276.

[23]  T. Vicsek,et al.  Clique percolation in random networks. , 2005, Physical review letters.

[24]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[25]  Carey E. Priebe,et al.  Community Detection and Classification in Hierarchical Stochastic Blockmodels , 2015, IEEE Transactions on Network Science and Engineering.

[26]  Weidi Dai,et al.  A multi-similarity spectral clustering method for community detection in dynamic networks , 2016, Scientific Reports.

[27]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[28]  Clara Pizzuti,et al.  Evolutionary Computation for Community Detection in Networks: A Review , 2018, IEEE Transactions on Evolutionary Computation.

[29]  Xiaochun Cao,et al.  Modularity Based Community Detection with Deep Learning , 2016, IJCAI.

[30]  Xiaochun Cao,et al.  Improving the Efficiency and Effectiveness of Community Detection via Prior-Induced Equivalent Super-Network , 2017, Scientific Reports.

[31]  Georgios B. Giannakis,et al.  Joint Community and Anomaly Tracking in Dynamic Networks , 2015, IEEE Transactions on Signal Processing.

[32]  Dong Liu,et al.  Semi-supervised community detection using label propagation , 2014 .

[33]  Weixiong Zhang,et al.  Modeling with Node Degree Preservation Can Accurately Find Communities , 2015, AAAI.

[34]  Robert D. Nowak,et al.  Majorization–Minimization Algorithms for Wavelet-Based Image Restoration , 2007, IEEE Transactions on Image Processing.

[35]  Lin Gao,et al.  Dynamic community detection based on network structural perturbation and topological similarity , 2017 .

[36]  Yun Chi,et al.  Facetnet: a framework for analyzing communities and their evolutions in dynamic networks , 2008, WWW.

[37]  Dong Liu,et al.  Effective Semisupervised Community Detection Using Negative Information , 2015 .

[38]  Cheng Wu,et al.  Targeted revision: A learning-based approach for incremental community detection in dynamic networks , 2016 .

[39]  Wenjun Wang,et al.  Temporal community detection based on symmetric nonnegative matrix factorization , 2017 .

[40]  Mark E. J. Newman,et al.  Stochastic blockmodels and community structure in networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  L. Mirny,et al.  Protein complexes and functional modules in molecular networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[42]  Pengfei Jiao,et al.  Constrained common cluster based model for community detection in temporal and multiplex networks , 2018, Neurocomputing.

[43]  Yi Shen,et al.  The similarity of weights on edges and discovering of community structure , 2014 .

[44]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[45]  Dino Pedreschi,et al.  Tiles: an online algorithm for community discovery in dynamic social networks , 2017, Machine Learning.

[46]  Jiawei Han,et al.  Multi-View Clustering via Joint Nonnegative Matrix Factorization , 2013, SDM.

[47]  Christos Faloutsos,et al.  RTM: Laws and a Recursive Generator for Weighted Time-Evolving Graphs , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[48]  Amedeo Caflisch,et al.  Efficient modularity optimization by multistep greedy algorithm and vertex mover refinement. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Rich Ling,et al.  “It’s just not that exciting anymore”: The changing centrality of SMS in the everyday lives of young Danes , 2016, New Media Soc..

[50]  Francesco Folino,et al.  An Evolutionary Multiobjective Approach for Community Discovery in Dynamic Networks , 2014, IEEE Transactions on Knowledge and Data Engineering.

[51]  Kevin S. Xu.  Stochastic Block Transition Models for Dynamic Networks , 2014, AISTATS.

[52]  Nam P. Nguyen,et al.  Dynamic Social Community Detection and Its Applications , 2014, PloS one.

[53]  Chris H. Q. Ding,et al.  Multi-document summarization via sentence-level semantic analysis and symmetric matrix factorization , 2008, SIGIR '08.

[54]  Laks V. S. Lakshmanan,et al.  Incremental cluster evolution tracking from highly dynamic network data , 2014, 2014 IEEE 30th International Conference on Data Engineering.

[55]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[56]  Yun Chi,et al.  On evolutionary spectral clustering , 2009, TKDD.

[57]  Deepayan Chakrabarti,et al.  Evolutionary clustering , 2006, KDD '06.