  Community detection in graphs has been extensively studied both in theory and
in applications. However, detecting communities in hypergraphs is more
challenging. In this paper, we propose a tensor decomposition approach for
guaranteed learning of communities in a special class of hypergraphs modeling
social tagging systems or folksonomies. A folksonomy is a tripartite 3-uniform
hypergraph consisting of (user, tag, resource) hyperedges. We posit a
probabilistic mixed membership community model, and prove that the tensor
method consistently learns the communities under efficient sample complexity
and separation requirements.
