Multilayer hypergraph clustering using the aggregate similarity matrix

TL;DR

This paper studies community detection in multilayer hypergraphs using an aggregated similarity matrix, proposing an SDP method with theoretical guarantees for exact recovery under certain conditions.

Contribution

It introduces an SDP-based approach for multilayer hypergraph clustering and provides information-theoretic conditions for guaranteed exact community recovery.

Findings

SDP approach achieves exact recovery under specified conditions.

Conditions cover both assortative and disassortative hypergraph cases.

Theoretical analysis extends to multilayer hypergraph models.

Abstract

We consider the community recovery problem on a multilayer variant of the hypergraph stochastic block model (HSBM). Each layer is associated with an independent realization of a d-uniform HSBM on N vertices. Given the similarity matrix containing the aggregated number of hyperedges incident to each pair of vertices, the goal is to obtain a partition of the N vertices into disjoint communities. In this work, we investigate a semidefinite programming (SDP) approach and obtain information-theoretic conditions on the model parameters that guarantee exact recovery both in the assortative and the disassortative cases.