Community detection in censored hypergraph
This addresses the problem of handling missing data in network analysis for researchers in machine learning and statistics, representing an incremental advance by extending existing methods to censored hypergraphs.
The paper tackles community detection in censored hypergraphs by deriving an information-theoretic threshold for exact recovery and proposing a polynomial-time algorithm that achieves this threshold using spectral methods with refinement.
Community detection refers to the problem of clustering the nodes of a network (either graph or hypergrah) into groups. Various algorithms are available for community detection and all these methods apply to uncensored networks. In practice, a network may has censored (or missing) values and it is shown that censored values have non-negligible effect on the structural properties of a network. In this paper, we study community detection in censored $m$-uniform hypergraph from information-theoretic point of view. We derive the information-theoretic threshold for exact recovery of the community structure. Besides, we propose a polynomial-time algorithm to exactly recover the community structure up to the threshold. The proposed algorithm consists of a spectral algorithm plus a refinement step. It is also interesting to study whether a single spectral algorithm without refinement achieves the threshold. To this end, we also explore the semi-definite relaxation algorithm and analyze its performance.