Random Walks on Hypergraphs with Edge-Dependent Vertex Weights

Autor:	Chitra, Uthsav, Raphael, Benjamin J
Rok vydání:	2019
Předmět:	Computer Science - Machine Learning Computer Science - Discrete Mathematics Computer Science - Social and Information Networks Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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 $\gamma_e(v)$ 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. Comment: Accepted to ICML 2019
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.08287 Zobrazit plný text záznamu View this record from Arxiv