Random walks on hypergraphs with edge-dependent vertex weights

Uthsav Chitra, Benjamin J. Raphael

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex weights: hypergraphs where every vertex v has a weight 7e(v) for each incident hyperedge e that describes the contribution of v to the hyperedge e. We derive a random walk-based hypergraph Laplacian, and bound the mixing time of random walks on such hypergraphs. Moreover, we give conditions under which random walks on such hypergraphs are equivalent to random walks on graphs. As a corollary, we show that current machine learning methods that rely on Laplacians derived from random walks on hypergraphs with edge-independent vertex weights do not utilize higher-order relationships in the data. Finally, we demonstrate the advantages of hypergraphs with edge-dependent vertex weights on ranking applications using real-world datasets.

Original languageEnglish (US)
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Pages2002-2011
Number of pages10
ISBN (Electronic)9781510886988
StatePublished - Jan 1 2019
Event36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
Duration: Jun 9 2019Jun 15 2019

Publication series

Name36th International Conference on Machine Learning, ICML 2019
Volume2019-June

Conference

Conference36th International Conference on Machine Learning, ICML 2019
CountryUnited States
CityLong Beach
Period6/9/196/15/19

All Science Journal Classification (ASJC) codes

  • Education
  • Computer Science Applications
  • Human-Computer Interaction

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    Chitra, U., & Raphael, B. J. (2019). Random walks on hypergraphs with edge-dependent vertex weights. In 36th International Conference on Machine Learning, ICML 2019 (pp. 2002-2011). (36th International Conference on Machine Learning, ICML 2019; Vol. 2019-June). International Machine Learning Society (IMLS).