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.

翻译：本文研究超图随机块模型（HSBM）多层变体上的社区恢复问题。每一层对应N个顶点上d均匀HSBM的独立实现。给定包含每对顶点关联超边聚合数量的相似度矩阵，目标是将N个顶点划分为不相交的社区。在本工作中，我们探究了半定规划（SDP）方法，并获得了模型参数的信息论条件，这些条件在同配与异配情形下均能保证精确恢复。