Multilayer hypergraph clustering using the aggregate similarity matrix

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.

arXiv comment16 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

References in corpus (8)

• Consistency of Spectral Hypergraph Partitioning under Planted Partition Model
• Clustering via Hypergraph Modularity
• Hypergraph Spectral Clustering in the Weighted Stochastic Block Model
• Statistical and computational phase transitions in spiked tensor estimation
• Spectral Detection on Sparse Hypergraphs
• Exact Recovery in the Hypergraph Stochastic Block Model: a Spectral Algorithm
• Community detection in the sparse hypergraph stochastic block model
• Robust Hypergraph Clustering via Convex Relaxation of Truncated MLE

Cited by in corpus (2)

• Optimal and exact recovery on the general nonuniform Hypergraph Stochastic Block Model
• Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model