Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clustering

@InProceedings{pmlr-v80-li18e,
  title = 	 {Submodular Hypergraphs: p-Laplacians, {C}heeger Inequalities and Spectral Clustering},
  author =       {Li, Pan and Milenkovic, Olgica},
  booktitle = 	 {Proceedings of the 35th International Conference on Machine Learning},
  pages = 	 {3014--3023},
  year = 	 {2018},
  editor = 	 {Dy, Jennifer and Krause, Andreas},
  volume = 	 {80},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {10--15 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v80/li18e/li18e.pdf},
  url = 	 {https://proceedings.mlr.press/v80/li18e.html},
  abstract = 	 {We introduce submodular hypergraphs, a family of hypergraphs that have different submodular weights associated with different cuts of hyperedges. Submodular hypergraphs arise in cluster- ing applications in which higher-order structures carry relevant information. For such hypergraphs, we define the notion of p-Laplacians and derive corresponding nodal domain theorems and k-way Cheeger inequalities. We conclude with the description of algorithms for computing the spectra of 1- and 2-Laplacians that constitute the basis of new spectral hypergraph clustering methods.}
}