Model-based clustering in simple hypergraphs through a stochastic blockmodel

Abstract

We present a new hypergraph stochastic blockmodel and an associated inference procedure for model-based clustering of the nodes in simple hypergraphs. Simple hypergraphs, where a node may not appear several times in a same hyperedge, have been overlooked in the literature, though they appropriately model some high-order interactions (such as co-authorship). The model assumes latent groups for the nodes and conditional independence of the hyperedges given the latent groups. We establish the first proof of generic identifiability of the parameters in such a model. We develop a variational approximation Expectation-Maximization algorithm for parameter inference and node clustering, and derive an integrated classification likelihood criterion for model selection. We illustrate the performance of our algorithm on synthetic data and analyse a real dataset of co-authorship. Our method called HyperSBM is implemented in C++ for efficiency and available as an R package at https://github.com/LB1304/HyperSBM.

Comparison of modularity-based approaches for nodes clustering in hypergraphs

“…It might be that the computational simplifications enabled by this assumption prevent from any attempt not to use it (see for e.g. Section B2 in Supplementary Material from Brusa and Matias, 2022b).…”

“…To conclude this introduction, we mention that there are other methods to cluster the nodes of a hypergraph, such as spectral clustering approaches (Chodrow et al, 2023;Ghoshdastidar and Dukkipati, 2017) or model-based methods (Brusa and Matias, 2022b;Ruggeri et al, 2023). It is also possible to cluster hyperedges instead of nodes (Ng and Murphy, 2022).…”

Commoning social–ecological networks through the lens of relational ontologies and other economies: How ecologists can diversify their notions of human–non-human relationships

“…Another choice of representation is the hypergraph, which works on all types of interactions (pairwise or otherwise), and has begun to garner some interest from ecologists (Golubski et al, 2016). However, the above-mentioned methods (ERGM and SBM) are not yet fully functional for the study of large hypergraphs (but see Brusa and Matias, 2022 for small hypergraph SBMs).…”

Community detection in large hypergraphs

“…Recently, statistical inference frameworks have been proposed to capture in a principled way the mesoscale organization of hypergraphs (35,50,51). Despite their success, current approaches suffer from a number of notable drawbacks.…”