Inferring community structure in attributed hypergraphs using stochastic
  block models
Kazuki Nakajima Takeaki Uno
Hypergraphs are a representation of complex systems involving interactions
among more than two entities and allow to investigation of higher-order
structure and dynamics in real-world complex systems. Community structure is a
common property observed in empirical networks in various domains. Stochastic
block models have been employed to investigate community structure in networks.
Node attribute data, often accompanying network data, has been found to
potentially enhance the learning of community structure in dyadic networks. In
this study, we develop a statistical framework that incorporates node attribute
data into the learning of community structure in a hypergraph, employing a
stochastic block model. We demonstrate that our model, which we refer to as
HyperNEO, enhances the learning of community structure in synthetic and
empirical hypergraphs when node attributes are sufficiently associated with the
communities. Furthermore, we found that applying a dimensionality reduction
method, UMAP, to the learned representations obtained using stochastic block
models, including our model, maps nodes into a two-dimensional vector space
while largely preserving community structure in empirical hypergraphs. We
expect that our framework will broaden the investigation and understanding of
higher-order community structure in real-world complex systems.