Community detection in censored hypergraph

TL;DR

This paper investigates community detection in censored hypergraphs, establishing theoretical thresholds for exact recovery and proposing efficient algorithms, including spectral and semi-definite relaxation methods.

Contribution

It introduces the first information-theoretic threshold for community detection in censored hypergraphs and proposes polynomial-time algorithms to achieve exact recovery.

Findings

Derived the information-theoretic threshold for exact community recovery.

Proposed a spectral algorithm with a refinement step for community detection.

Analyzed the performance of semi-definite relaxation algorithms in this context.

Abstract

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.