Multilayer hypergraph clustering using the aggregate similarity matrix
arXiv:2301.11657 · doi:10.1007/978-3-031-32296-9_6
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.
16 pages, 3 tables. Reason for replacement on 3 Nov 2023: incorporating the possibility of non-uniform layers. Reason for replacement on 18 May 2023: improving clarity of the presentation and clarifying the contribution/novelty of the paper