Information Limits for Community Detection in Hypergraph with Label Information

Xiaofeng Zhao, Wei Zhao, Mingao Yuan
2021 Symmetry  
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
more » ... el (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.
doi:10.3390/sym13112060 fatcat:7vl23xhponeljnfbyorm5lbvbi