We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with each vertex-hyperedge pair, yielding a weighted incidence matrix of the hypergraph. Such weightings have been utilized in term-document representations of text data sets. We explain how random walks with EDVW serve to construct different hypergraph Laplacian matrices, and then develop a suite of clustering methods that use these incidence matrices and Laplacians for hypergraph clustering. Using several data sets from real-life applications, we compare the performance of these clustering algorithms experimentally against a variety of existing hypergraph clustering methods. We show that the proposed methods produce higher-quality clusters and conclude by highlighting avenues for future work.

中文翻译：

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超图随机游走、拉普拉斯算子和聚类

我们提出了一个灵活的框架，用于基于最近提出的利用边缘相关顶点权重的随机游走对超图结构数据进行聚类。当结合边相关顶点权重（EDVW）时，权重与每个顶点-超边对相关联，产生超图的加权关联矩阵。这种权重已被用于文本数据集的术语文档表示。我们解释了 EDVW 随机游走如何用于构建不同的超图拉普拉斯矩阵，然后开发一套聚类方法，使用这些关联矩阵和拉普拉斯算子进行超图聚类。使用来自现实生活应用程序的几个数据集，我们通过实验将这些聚类算法的性能与各种现有的超图聚类方法进行了比较。