We propose a model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co-authorship datasets. Our model generalizes the stochastic blockmodel for graphs and assumes the existence of latent node groups and hyperedges are conditionally independent given these groups. We first establish the generic identifiability of the model parameters. We then develop a variational approximation Expectation-Maximization algorithm for parameter inference and node clustering, and derive a statistical criterion for model selection. To illustrate the performance of our R package HyperSBM, we compare it with other node clustering methods using synthetic data generated from the model, as well as from a line clustering experiment and a co-authorship dataset.

翻译：我们提出一种模型，用于解决简单超图中被忽视的节点聚类问题。简单超图适用于同一节点在超边中不会重复出现的场景（如合著数据集）。该模型将图的随机块模型进行推广，假设存在潜在节点分组，且超边在这些分组条件下具有条件独立性。我们首先建立模型参数的通用可识别性，随后开发了用于参数推断和节点聚类的变分近似期望最大化算法，并推导出模型选择的统计准则。为验证R包HyperSBM的性能，我们将其与基于模型生成的合成数据、线性聚类实验数据以及合著数据集的其他节点聚类方法进行对比。