ELRUHNA: Elimination Rule-basedHypergraph Alignment

2025-06-11

AI Summary

Hypergraph alignment is an NP-hard problem with critical applications in bioinformatics, social networks, and computer vision; however, existing work remains scarce and lacks scalable solutions. This paper proposes the first unsupervised hypergraph alignment framework: it models hypergraphs as bipartite graphs and jointly optimizes vertex and hyperedge alignments. We introduce *incidence-aware alignment*, a novel modeling paradigm that integrates local matching with an annealing-based similarity propagation mechanism, initialized via generalized eigenvector centrality to enhance convergence. Additionally, we design an elimination-rule-based heuristic search to accelerate optimization. Evaluated on multiple real-world datasets, our method achieves statistically significant improvements in alignment accuracy over state-of-the-art approaches, while demonstrating strong scalability—enabling efficient alignment of large-scale hypergraphs.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Hypergraph alignment is NP-hard with practical applications
• Scalable solutions needed for high-order relational data analysis
• Unsupervised hypergraph alignment lacks efficient methods compared to graphs

Innovation

• Elimination rule-based hypergraph alignment framework
• Binary quadratic optimization for vertex alignment
• Similarity propagation with local matching rules