Community Recovery in Hypergraphs

Data clustering is a core problem in many fields of science and engineering. Community recovery in graphs is one popular approach to data clustering, and it has received significant attention due to its wide applicability to social network applications, protein complex detection, shape matching, image segmentation, etc. While the community recovery in graphs has been extensively studied in the literature, the problem of community recovery in hypergraphs has not been studied much. In this paper, we study the generalized Censored Block Model (CBM), where observations consist of randomly chosen hyperedges of size d, each of which is associated with the modulo-2 sum of the values of the nodes in the hyperedge, corrupted by Bernoulli noise. We characterize the information-theoretic limit of the community recovery in hypergraphs. Our results are for the general cases of arbitrarily scaling d.