Consistency of Spectral Hypergraph Partitioning under Planted Partition Model

TL;DR

This paper introduces a planted partition model for sparse non-uniform hypergraphs and establishes the first consistency results for spectral hypergraph partitioning under this model, extending theoretical understanding in hypergraph clustering.

Contribution

It develops a planted partition model for non-uniform hypergraphs and proves a novel consistency result for spectral hypergraph partitioning algorithms.

Findings

Derived an error bound for spectral hypergraph partitioning.

Established the first consistency result for non-uniform hypergraph partitioning.

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 non-uniform 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 non-uniform hypergraphs.