Discovery of path-important nodes using structured semi-nonnegative matrix factorization

Identifying critical components in networked systems is a key problem for many important applications in a diverse set of fields, including epidemiology, e-commerce and traffic systems. This paper describes the development and application of a semi-nonnegative matrix factorization for structural discovery featuring nodes that are important for transmission over social networks. The technique allows the practitioner to perform structured matrix factorization by specifying context-specific network statistics that guide the solution. The techniques are demonstrated on a network derived from Twitter data.

[1]  Chris H. Q. Ding,et al.  On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering , 2005, SDM.

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

[3]  Chris H. Q. Ding,et al.  On the equivalence between Non-negative Matrix Factorization and Probabilistic Latent Semantic Indexing , 2008, Comput. Stat. Data Anal..

[4]  R. Plemmons,et al.  Optimality, computation, and interpretation of nonnegative matrix factorizations , 2004 .

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

[6]  Bin Yu,et al.  Co-clustering for directed graphs: the Stochastic co-Blockmodel and spectral algorithm Di-Sim , 2012, 1204.2296.

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

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

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

[10]  Hyunsoo Kim,et al.  Nonnegative Matrix Factorization Based on Alternating Nonnegativity Constrained Least Squares and Active Set Method , 2008, SIAM J. Matrix Anal. Appl..

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

[12]  Ulrik Brandes,et al.  Network ensemble clustering using latent roles , 2011, Adv. Data Anal. Classif..

[13]  Chris H. Q. Ding,et al.  Convex and Semi-Nonnegative Matrix Factorizations , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Derek Greene,et al.  Producing a unified graph representation from multiple social network views , 2013, WebSci.