Hypergraphs are a natural modeling paradigm for a wide range of complex
relational systems. A standard analysis task is to identify clusters of closely
related or densely interconnected nodes. Many graph algorithms for this task
are based on variants of the stochastic blockmodel, a random graph with
flexible cluster structure. However, there are few models and algorithms for
hypergraph clustering. Here, we propose a Poisson degree-corrected hypergraph
stochastic blockmodel (DCHSBM), a generative model of clustered hypergraphs
with heterogeneous node degrees and edge sizes. Approximate maximum-likelihood
inference in the DCHSBM naturally leads to a clustering objective that
generalizes the popular modularity objective for graphs. We derive a general
Louvain-type algorithm for this objective, as well as a a faster, specialized
"All-Or-Nothing" (AON) variant in which edges are expected to lie fully within
clusters. This special case encompasses a recent proposal for modularity in
hypergraphs, while also incorporating flexible resolution and edge-size
parameters. We show that AON hypergraph Louvain is highly scalable, including
as an example an experiment on a synthetic hypergraph of one million nodes. We
also demonstrate through synthetic experiments that the detectability regimes
for hypergraph community detection differ from methods based on dyadic graph
projections. We use our generative model to analyze different patterns of
higher-order structure in school contact networks, U.S. congressional bill
cosponsorship, U.S. congressional committees, product categories in
co-purchasing behavior, and hotel locations from web browsing sessions, finding
interpretable higher-order structure. We then study the behavior of our AON
hypergraph Louvain algorithm, finding that it is able to recover ground truth
clusters in empirical data sets exhibiting the corresponding higher-order
structure.

本文提出了一种基于泊松度校正超图随机块模型（DCHSBM）的聚类方法，该方法利用最大似然推断来实现超图聚类，其聚类目标扩展了图的流行性目标，使用了一种新的基于节点整合的变化，具有高可扩展性。通过综合分析各种实验数据，包括学校联系网络、U.S. 国会议案、合作购买行为的产品类别和网站浏览会话的酒店位置，作者发现该聚类方法能够恢复具有相应高阶结构的真实聚类。