Automatic Dimension Selection for a Non-negative Factorization Approach   to Clustering Multiple Random Graphs
  We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare its performance with two standard clustering algorithms. 
Nam H. Lee and I-Jeng Wang and Youngser Park and Care E. Priebe and   Michael Rosen
stat.ML