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February 2017 Consistency of spectral hypergraph partitioning under planted partition model
Debarghya Ghoshdastidar, Ambedkar Dukkipati
Ann. Statist. 45(1): 289-315 (February 2017). DOI: 10.1214/16-AOS1453

Abstract

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under the stochastic block model are well known. In this paper, we present a planted partition model for sparse random nonuniform hypergraphs that generalizes the stochastic block model. We derive an error bound for a spectral hypergraph partitioning algorithm under this model using matrix concentration inequalities. To the best of our knowledge, this is the first consistency result related to partitioning nonuniform hypergraphs.

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Debarghya Ghoshdastidar. Ambedkar Dukkipati. "Consistency of spectral hypergraph partitioning under planted partition model." Ann. Statist. 45 (1) 289 - 315, February 2017. https://doi.org/10.1214/16-AOS1453

Information

Received: 1 May 2015; Revised: 1 February 2016; Published: February 2017
First available in Project Euclid: 21 February 2017

zbMATH: 1360.62330
MathSciNet: MR3611493
Digital Object Identifier: 10.1214/16-AOS1453

Subjects:
Primary: 62F12 , 62H30
Secondary: 05C65 , 05C80

Keywords: Hypergraph , spectral algorithm , Stochastic block model

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 1 • February 2017
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