## The Annals of Statistics

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

### Consistency of spectral hypergraph partitioning under planted partition model

Debarghya Ghoshdastidar and Ambedkar Dukkipati

#### 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

#### 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.Digital Object Identifier: doi:10.1214/16-AOS1453SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.