ELRUHNA: Elimination Rule-basedHypergraph Alignment

TL;DR

ELRUHNA is an unsupervised, elimination rule-based framework for hypergraph alignment that effectively handles high-order data, outperforming existing methods in accuracy and scalability.

Contribution

The paper introduces ELRUHNA, a novel hypergraph alignment method using incidence-based optimization and similarity propagation, addressing scalability and accuracy issues in hypergraph matching.

Findings

ELRUHNA outperforms state-of-the-art algorithms in accuracy.

It scales effectively to large hypergraphs.

The method demonstrates robustness on real-world datasets.

Abstract

Hypergraph alignment is a well-known NP-hard problem with numerous practical applications across domains such as bioinformatics, social network analysis, and computer vision. Despite its computational complexity, practical and scalable solutions are urgently needed to enable pattern discovery and entity correspondence in high-order relational data. The problem remains understudied in contrast to its graph based counterpart. In this paper, we propose ELRUHNA, an elimination rule-based framework for unsupervised hypergraph alignment that operates on the bipartite representation of hypergraphs. We introduce the incidence alignment formulation, a binary quadratic optimization approach that jointly aligns vertices and hyperedges. ELRUHNA employs a novel similarity propagation scheme using local matching and cooling rules, supported by an initialization strategy based on generalized eigenvector centrality for incidence matrices. Through extensive experiments on real-world datasets, we demonstrate that ELRUHNA achieves higher alignment accuracy compared to state-of-the-art algorithms, while scaling effectively to large hypergraphs.