The Annals of Statistics

Consistency of spectral hypergraph partitioning under planted partition model

Debarghya Ghoshdastidar and Ambedkar Dukkipati

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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.

Article information

Source
Ann. Statist., Volume 45, Number 1 (2017), 289-315.

Dates
Received: May 2015
Revised: February 2016
First available in Project Euclid: 21 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.aos/1487667624

Digital Object Identifier
doi:10.1214/16-AOS1453

Mathematical Reviews number (MathSciNet)
MR3611493

Zentralblatt MATH identifier
1360.62330

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 62F12: Asymptotic properties of estimators
Secondary: 05C65: Hypergraphs 05C80: Random graphs [See also 60B20]

Keywords
Hypergraph stochastic block model spectral algorithm

Citation

Ghoshdastidar, Debarghya; Dukkipati, Ambedkar. Consistency of spectral hypergraph partitioning under planted partition model. Ann. Statist. 45 (2017), no. 1, 289--315. doi:10.1214/16-AOS1453. https://projecteuclid.org/euclid.aos/1487667624


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Supplemental materials

  • Supplement to “Consistency of spectral hypergraph partitioning under planted partition model”. The supplementary material contains detailed proofs of all the lemmas and corollaries stated in Sections 4 and 5.