Uncovering Community Structures with Initialized Bayesian Nonnegative Matrix Factorization

Uncovering community structures is important for understanding networks. Currently, several nonnegative matrix factorization algorithms have been proposed for discovering community structure in complex networks. However, these algorithms exhibit some drawbacks, such as unstable results and inefficient running times. In view of the problems, a novel approach that utilizes an initialized Bayesian nonnegative matrix factorization model for determining community membership is proposed. First, based on singular value decomposition, we obtain simple initialized matrix factorizations from approximate decompositions of the complex network’s adjacency matrix. Then, within a few iterations, the final matrix factorizations are achieved by the Bayesian nonnegative matrix factorization method with the initialized matrix factorizations. Thus, the network’s community structure can be determined by judging the classification of nodes with a final matrix factor. Experimental results show that the proposed method is highly accurate and offers competitive performance to that of the state-of-the-art methods even though it is not designed for the purpose of modularity maximization.

[1]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Carlo Tomasi,et al.  Singular Value Decomposition , 2021, Encyclopedia of Social Network Analysis and Mining.

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

[4]  David M Blei,et al.  Efficient discovery of overlapping communities in massive networks , 2013, Proceedings of the National Academy of Sciences.

[5]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Dit-Yan Yeung,et al.  Overlapping community detection via bounded nonnegative matrix tri-factorization , 2012, KDD.

[7]  P. Ronhovde,et al.  Multiresolution community detection for megascale networks by information-based replica correlations. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Stephen J. Roberts,et al.  Variational Mixture of Bayesian Independent Component Analyzers , 2003, Neural Computation.

[9]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[10]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Stefan M. Wild.  Seeding Non-Negative Matrix Factorizations with the Spherical K-Means Clustering , 2003 .

[12]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[13]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[14]  David Mackay,et al.  Probable networks and plausible predictions - a review of practical Bayesian methods for supervised neural networks , 1995 .

[15]  Ioannis Psorakis,et al.  Soft Partitioning in Networks via Bayesian Non-negative Matrix Factorization , 2010 .

[16]  Christos Boutsidis,et al.  SVD based initialization: A head start for nonnegative matrix factorization , 2008, Pattern Recognit..

[17]  A Díaz-Guilera,et al.  Self-similar community structure in a network of human interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  M. Newman.  Erratum: Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality (Physical Review e (2001) 64 (016132)) , 2006 .

[19]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[20]  Lada A. Adamic,et al.  The political blogosphere and the 2004 U.S. election: divided they blog , 2005, LinkKDD '05.

[21]  John B. Moore,et al.  Singular Value Decomposition , 1994 .

[22]  David Lusseau,et al.  The emergent properties of a dolphin social network , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[23]  Andrea Lancichinetti,et al.  Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Javier Béjar,et al.  Clustering algorithm for determining community structure in large networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[26]  Bruce A. Weinberg,et al.  Social Interactions with Endogenous Associations , 2007 .

[27]  Andrea Lancichinetti,et al.  Detecting the overlapping and hierarchical community structure in complex networks , 2008, 0802.1218.

[28]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[29]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[30]  Yixin Cao,et al.  Identifying overlapping communities as well as hubs and outliers via nonnegative matrix factorization , 2013, Scientific Reports.

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

[32]  Stephen J. Roberts,et al.  Data decomposition using independent component analysis with prior constraints , 2003, Pattern Recognit..

[33]  Andrea Lancichinetti,et al.  Erratum: Community detection algorithms: A comparative analysis [Phys. Rev. E 80, 056117 (2009)] , 2014 .

[34]  Michael W. Berry,et al.  Algorithms and applications for approximate nonnegative matrix factorization , 2007, Comput. Stat. Data Anal..

[35]  Stephen J. Roberts,et al.  Bayesian Independent Component Analysis with Prior Constraints: An Application in Biosignal Analysis , 2004, Deterministic and Statistical Methods in Machine Learning.

[36]  Stephen Roberts,et al.  Overlapping community detection using Bayesian non-negative matrix factorization. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  C. Févotte,et al.  Automatic Relevance Determination in Nonnegative Matrix Factorization , 2009 .

[38]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[39]  Amy Nicole Langville,et al.  Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization , 2014, ArXiv.

[40]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.