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.
Pan Li (University of Illinois Urbana-Champaign)
Olgica Milenkovic (University of Illinois UC)
Related Events (a corresponding poster, oral, or spotlight)
2018 Oral: Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clustering »
Fri Jul 13th 02:40 -- 02:50 PM Room K11