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- W4300528977 abstract "We study p-Laplacians and spectral clustering for a recently proposed hypergraph model that incorporates edge-dependent vertex weights (EDVW). These weights can reflect different importance of vertices within a hyperedge, thus conferring the hypergraph model higher expressivity and flexibility. By constructing submodular EDVW-based splitting functions, we convert hypergraphs with EDVW into submodular hypergraphs for which the spectral theory is better developed. In this way, existing concepts and theorems such as p-Laplacians and Cheeger inequalities proposed under the submodular hypergraph setting can be directly extended to hypergraphs with EDVW. For submodular hypergraphs with EDVW-based splitting functions, we propose an efficient algorithm to compute the eigenvector associated with the second smallest eigenvalue of the hypergraph 1-Laplacian. We then utilize this eigenvector to cluster the vertices, achieving higher clustering accuracy than traditional spectral clustering based on the 2-Laplacian. More broadly, the proposed algorithm works for all submodular hypergraphs that are graph reducible. Numerical experiments using real-world data demonstrate the effectiveness of combining spectral clustering based on the 1-Laplacian and EDVW." @default.
- W4300528977 created "2022-10-03" @default.
- W4300528977 creator A5012007074 @default.
- W4300528977 creator A5071894027 @default.
- W4300528977 date "2022-08-15" @default.
- W4300528977 modified "2023-10-18" @default.
- W4300528977 title "Hypergraphs with Edge-Dependent Vertex Weights: p-Laplacians and Spectral Clustering" @default.
- W4300528977 doi "https://doi.org/10.48550/arxiv.2208.07457" @default.
- W4300528977 hasPublicationYear "2022" @default.
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