Overlapping Communities and the Prediction of Missing Links in Multiplex Networks

Multiplex networks are a representation of real-world complex systems as a set of entities (i.e. nodes) connected via different types of connections (i.e. layers). The observed connections in these networks may not be complete and the link prediction task is about locating the missing links across layers. Here, the main challenge is about collecting relevant evidence from different layers to assist the link prediction task. It is known that co-membership in communities increases the likelihood of connectivity between nodes. We discuss that co-membership in the communities of the similar layers augments the chance of connectivity. The layers are considered similar if they show significant inter-layer community overlap. Moreover, we found that although the presence of link is correlated in layers but the extent of this correlation is not the same across different communities. Our proposed, ML-BNMTF, as a link prediction method in multiplex networks, is devised based on these findings. ML-BNMTF outperforms baseline methods specifically when the global link overlap is low.

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

[2]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[3]  Mahdi Jalili,et al.  Link Prediction in Multiplex Networks based on Interlayer Similarity , 2019, Physica A: Statistical Mechanics and its Applications.

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

[5]  M. Newman,et al.  Hierarchical structure and the prediction of missing links in networks , 2008, Nature.

[6]  R. Guimerà,et al.  The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

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

[10]  Ginestra Bianconi,et al.  Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Mahdi Jalili,et al.  Link prediction in multiplex online social networks , 2017, Royal Society Open Science.

[12]  Mahdi Jalili,et al.  Application of hyperbolic geometry in link prediction of multiplex networks , 2019, Scientific Reports.

[13]  Jure Leskovec,et al.  Defining and evaluating network communities based on ground-truth , 2012, Knowledge and Information Systems.

[14]  D. Chklovskii,et al.  Wiring optimization can relate neuronal structure and function. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

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

[16]  Henrik Jeldtoft Jensen,et al.  Comparison of Communities Detection Algorithms for Multiplex , 2014, ArXiv.

[17]  Peng Wang,et al.  Link prediction in social networks: the state-of-the-art , 2014, Science China Information Sciences.

[18]  Alireza Hajibagheri,et al.  A Holistic Approach for Link Prediction in Multiplex Networks , 2016, SocInfo.

[19]  Rushed Kanawati,et al.  Link prediction in multiplex networks , 2015, Networks Heterog. Media.

[20]  Malik Magdon-Ismail,et al.  Efficient Identification of Overlapping Communities , 2005, ISI.

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

[22]  V. Carchiolo,et al.  Extending the definition of modularity to directed graphs with overlapping communities , 2008, 0801.1647.

[23]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[24]  Ana L. N. Fred,et al.  Robust data clustering , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[25]  Linyuan Lu,et al.  Link Prediction in Complex Networks: A Survey , 2010, ArXiv.

[26]  Boleslaw K. Szymanski,et al.  Overlapping community detection in networks: The state-of-the-art and comparative study , 2011, CSUR.

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

[28]  Shihua Zhang,et al.  Identification of overlapping community structure in complex networks using fuzzy c-means clustering , 2007 .

[29]  Vito Latora,et al.  Measuring and modelling correlations in multiplex networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[31]  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.

[32]  Massimiliano Zanin,et al.  Emergence of network features from multiplexity , 2012, Scientific Reports.

[33]  Vito Latora,et al.  Emergence of Multiplex Communities in Collaboration Networks , 2015, PloS one.

[34]  Mason A. Porter,et al.  Edge Correlations in Multilayer Networks , 2019, ArXiv.

[35]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[36]  G. Bianconi.  Statistical mechanics of multiplex networks: entropy and overlap. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  M. Emiliani,et al.  Terrorism in Indonesia: Noordin's Networks , 2009 .

[38]  Jure Leskovec,et al.  Overlapping community detection at scale: a nonnegative matrix factorization approach , 2013, WSDM.

[39]  Nitesh V. Chawla,et al.  Multi-relational Link Prediction in Heterogeneous Information Networks , 2011, 2011 International Conference on Advances in Social Networks Analysis and Mining.

[40]  Lav R. Varshney,et al.  Structural Properties of the Caenorhabditis elegans Neuronal Network , 2009, PLoS Comput. Biol..

[41]  J. Hanley,et al.  A method of comparing the areas under receiver operating characteristic curves derived from the same cases. , 1983, Radiology.

[42]  Alex Arenas,et al.  Analysis of the structure of complex networks at different resolution levels , 2007, physics/0703218.

[43]  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.

[44]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[45]  Cristopher Moore,et al.  Community detection, link prediction, and layer interdependence in multilayer networks , 2017, Physical review. E.

[46]  Vito Latora,et al.  Structural measures for multiplex networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Kwang-Il Goh,et al.  Towards real-world complexity: an introduction to multiplex networks , 2015, ArXiv.

[48]  P. Bork,et al.  Functional organization of the yeast proteome by systematic analysis of protein complexes , 2002, Nature.

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

[50]  Yabing Yao,et al.  Link prediction via layer relevance of multiplex networks , 2017 .

[51]  Evgeniy Gabrilovich,et al.  A Review of Relational Machine Learning for Knowledge Graphs , 2015, Proceedings of the IEEE.

[52]  Cecilia Mascolo,et al.  A multilayer approach to multiplexity and link prediction in online geo-social networks , 2016, EPJ Data Science.