Information Limits for Community Detection in Hypergraph with Label Information

In network data mining, community detection refers to the problem of partitioning the nodes of a network into clusters (communities). This is equivalent to identifying the cluster label of each node. A label estimator is said to be an exact recovery of the true labels (communities) if it coincides with the true labels with a probability convergent to one. In this work, we consider the effect of label information on the exact recovery of communities in an m-uniform Hypergraph Stochastic Block Model (HSBM). We investigate two scenarios of label information: (1) a noisy label for each node is observed independently, with 1−αn as the probability that the noisy label will match the true label; (2) the true label of each node is observed independently, with the probability of 1−αn. We derive sharp boundaries for exact recovery under both scenarios from an information-theoretical point of view. The label information improves the sharp detection boundary if and only if αn=n−β+o(1) for a constant β>0.