Residuals-based subgraph detection with cue vertices

A common problem in modern graph analysis is the detection of communities, an example of which is the detection of a single anomalously dense subgraph. Recent results have demonstrated a fundamental limit for this problem when using spectral analysis of modularity. In this paper, we demonstrate the implication of these results on subgraph detection when a cue vertex is provided, indicating one of the vertices in the community of interest. Several recent algorithms for local community detection are applied in this context, and we compare their empirical performance to that of the simple method used to derive the theoretical detection limits.

[1]  Fan Chung Graham,et al.  Local Graph Partitioning using PageRank Vectors , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[2]  Raj Rao Nadakuditi,et al.  On hard limits of eigen-analysis based planted clique detection , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[3]  Nisheeth K. Vishnoi,et al.  A local spectral method for graphs: with applications to improving graph partitions and exploring data graphs locally , 2009, J. Mach. Learn. Res..

[4]  Patrick J. Wolfe,et al.  A Spectral Framework for Anomalous Subgraph Detection , 2014, IEEE Transactions on Signal Processing.

[5]  Carey E. Priebe,et al.  Vertex Nomination via Content and Context , 2012, ArXiv.

[6]  Nisheeth K. Vishnoi,et al.  A Spectral Algorithm for Improving Graph Partitions , 2009, ArXiv.

[7]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.

[8]  Steven Thomas Smith,et al.  Bayesian Discovery of Threat Networks , 2013, IEEE Transactions on Signal Processing.

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

[10]  E. Arias-Castro,et al.  Community Detection in Random Networks , 2013, 1302.7099.

[11]  Jennifer Widom,et al.  Scaling personalized web search , 2003, WWW '03.