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 aggregated number of hyperedges incident to each pair of vertices, represented using a similarity matrix, 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.

翻译：我们考虑超图随机块模型（HSBM）多层变体上的群落恢复问题。每个层对应于在N个顶点上独立生成的d-均匀HSBM实现。给定基于相似度矩阵表示的每对顶点间超边聚合数量，目标是将N个顶点划分为互不相交的群落。本研究采用半定规划（SDP）方法，获得了在齐次（assortative）与非齐次（disassortative）情形下保证精确恢复的模型参数信息论条件。