@inproceedings{d4914df78c3b4e2f9482a813ad944f0e,
title = "Submodular hypergraphs: P-Laplacians, cheeger inequalities and spectral clustering",
abstract = "We introduce submodular hypergraphs, a family of hypergraphs that have different sub- modular weights associated with different cuts of hyperedges. Submodular hypergraphs arise in clustering 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.",
author = "Pan Li and Olgica Milenkovic",
note = "Publisher Copyright: {\textcopyright} Copyright 2018 by the author(s).; 35th International Conference on Machine Learning, ICML 2018 ; Conference date: 10-07-2018 Through 15-07-2018",
year = "2018",
language = "English (US)",
series = "35th International Conference on Machine Learning, ICML 2018",
publisher = "International Machine Learning Society (IMLS)",
pages = "4690--4719",
editor = "Jennifer Dy and Andreas Krause",
booktitle = "35th International Conference on Machine Learning, ICML 2018",
}