Community Detection With Known, Unknown, or Partially Known Auxiliary Latent Variables

Empirical observations suggest that in practice, community membership does not completely explain the dependency between edges of an observation graph. The residual dependence graph are modeled this paper, to first order, by auxiliary node latent variables affect statistics but carry no information about communities interest. We then study detection graphs obeying stochastic block model and censored with variables. analyze conditions for exact recovery when these unknown, representing unknown nuisance parameters or mismatch. also secondary have been either fully partially revealed. Finally, we propose a semidefinite programming algorithm recovering desired labels known unknown. show is possible down respective maximum likelihood threshold.