A fast and robust kernel optimization method for core–periphery detection in directed and weighted graphs

Many graph mining tasks can be viewed as classification problems on high dimensional data. Within this class we consider the issue of discovering core-periphery structure, which has wide applications in the economic and social sciences. In contrast to many current approaches, we allow for weighted and directed edges and we do not assume that the overall network is connected. Our approach extends recent work on a relevant relaxed nonlinear optimization problem. In the directed, weighted setting, we derive and analyze a globally convergent iterative algorithm. We also relate the algorithm to a maximum likelihood reordering problem on an appropriate core-periphery random graph model. We illustrate the effectiveness of the new algorithm on a large scale directed email network.

[1]  Song Yang,et al.  Networks: An Introduction by M. E. J. Newman , 2013 .

[2]  Mason A. Porter,et al.  Core-Periphery Structure in Networks , 2012, SIAM J. Appl. Math..

[3]  M. Newman.  Community detection in networks: Modularity optimization and maximum likelihood are equivalent , 2016, Physical review. E.

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  Carlos J. Melián,et al.  The nested assembly of plant–animal mutualistic networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Sang Hoon Lee,et al.  Detection of core–periphery structure in networks using spectral methods and geodesic paths , 2014, European Journal of Applied Mathematics.

[7]  Peter D. Hoff,et al.  Latent Space Approaches to Social Network Analysis , 2002 .

[8]  Austin R. Benson,et al.  Random Spatial Network Models for Core-Periphery Structure , 2018, WSDM.

[9]  E. Liu,et al.  Large-Scale Functional Organization of Long-Range Chromatin Interaction Networks , 2012, Cell reports.

[10]  Mason A. Porter,et al.  Core-Periphery Structure in Networks (Revisited) , 2017, SIAM Rev..

[11]  Desmond J. Higham,et al.  A Nonlinear Spectral Method for Core-Periphery Detection in Networks , 2018, SIAM J. Math. Data Sci..

[12]  Ning Wang,et al.  Diffusion Dynamics with Changing Network Composition , 2013, Entropy.

[13]  Bas Lemmens,et al.  Nonlinear Perron-Frobenius Theory , 2012 .

[14]  Andrew M. Stuart,et al.  Uncertainty Quantification in Graph-Based Classification of High Dimensional Data , 2017, SIAM/ASA J. Uncertain. Quantification.

[15]  Yiming Yang,et al.  The Enron Corpus: A New Dataset for Email Classi(cid:12)cation Research , 2004 .

[16]  Shi Zhou,et al.  The rich-club phenomenon in the Internet topology , 2003, IEEE Communications Letters.

[17]  Martin G. Everett,et al.  Models of core/periphery structures , 2000, Soc. Networks.

[18]  Raul J. Mondragón,et al.  Network partition via a bound of the spectral radius , 2015, J. Complex Networks.

[19]  Hans J. Herrmann,et al.  Mitigation of malicious attacks on networks , 2011, Proceedings of the National Academy of Sciences.

[20]  Frank Schweitzer,et al.  The Rise and Fall of R&D Networks , 2013, ArXiv.

[21]  Fabio Della Rossa,et al.  Profiling core-periphery network structure by random walkers , 2013, Scientific Reports.

[22]  Ling-Yun Wu,et al.  Structure and dynamics of core/periphery networks , 2013, J. Complex Networks.

[23]  S. Feizi,et al.  Maximum Likelihood Latent Space Embedding of Logistic Random Dot Product Graphs , 2015, 1510.00850.

[24]  Mondragon-Ceballos.  Network partition via a bound of the spectral radius , 2018 .

[25]  Andrew M. Stuart,et al.  Uncertainty Quantification in the Classification of High Dimensional Data , 2017, ArXiv.

[26]  Jan O. Korbel,et al.  Positive selection at the protein network periphery: Evaluation in terms of structural constraints and cellular context , 2007, Proceedings of the National Academy of Sciences.