We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs). In this hypergraph model, the contribution of every vertex to each of its incident hyperedges is represented through an edge-dependent weight, conferring the model higher expressivity than the classical hypergraph. In our method, we leverage random walks with EDVWs to construct a hypergraph Laplacian and use its spectral properties to embed vertices and hyperedges in a common space. We then cluster these embeddings to obtain our proposed co-clustering method, of particular relevance in applications requiring the simultaneous clustering of data entities and features. Numerical experiments using real-world data demonstrate the effectiveness of our proposed approach in comparison with state-of-the-art alternatives.

中文翻译：

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通过谱图超图分割对顶点和超边进行聚类

我们提出了一种新颖的方法来将超图的顶点和超边与边缘相关的顶点权重（EDVWs）共同聚类。在此超图模型中，每个顶点对其每个入射超边的贡献通过边依赖的权重表示，赋予模型比经典超图更高的表现力。在我们的方法中，我们利用带有EDVW的随机游走来构造超图拉普拉斯算子，并使用其光谱特性将顶点和超边嵌入到公共空间中。然后，我们对这些嵌入进行聚类以获得我们提出的共聚方法，该方法在需要同时对数据实体和特征进行聚类的应用程序中特别相关。使用实际数据进行的数值实验证明了我们提出的方法与最新技术相比的有效性。