Effective and Efficient Attributed Hypergraph Embedding on Nodes and Hyperedges

2025-08-12

AI Summary

To address the low-quality joint embedding and poor scalability for nodes and hyperedges in large-scale attributed hypergraphs, this paper proposes SAHE. The method introduces two novel high-order similarity measures—HMS-N for node pairs and HMS-E for hyperedge pairs—and constructs an expanded hypergraph to capture multi-hop associations and global topology. It further devises a unified approximate optimization framework that jointly preserves all high-order similarities without explicitly forming dense matrices. Extensive experiments on multiple real-world attributed hypergraph datasets demonstrate that SAHE significantly outperforms 11 state-of-the-art baselines across tasks including node classification and hyperedge link prediction. It achieves substantial improvements in embedding quality while accelerating training by several orders of magnitude. SAHE thus offers superior efficiency, scalability, and practical applicability for large-scale attributed hypergraph representation learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

An attributed hypergraph comprises nodes with attributes and hyperedges that connect varying numbers of nodes. Attributed hypergraph node and hyperedge embedding (AHNEE) maps nodes and hyperedges to compact vectors for use in important tasks such as node classification, hyperedge link prediction, and hyperedge classification. Generating high-quality embeddings is challenging due to the complexity of attributed hypergraphs and the need to embed both nodes and hyperedges, especially in large-scale data. Existing solutions often fall short by focusing only on nodes or lacking native support for attributed hypergraphs, leading to inferior quality, and struggle with scalability on large attributed hypergraphs. We propose SAHE, an efficient and effective approach that unifies node and hyperedge embeddings for AHNEE computation, advancing the state of the art via comprehensive embedding formulations and algorithmic designs. First, we introduce two higher-order similarity measures, HMS-N and HMS-E, to capture similarities between node pairs and hyperedge pairs, respectively. These measures consider multi-hop connections and global topology within an extended hypergraph that incorporates attribute-based hyperedges. SAHE formulates the AHNEE objective to jointly preserve all-pair HMS-N and HMS-N similarities. Direct optimization is computationally expensive, so we analyze and unify core approximations of all-pair HMS-N and HMS-N to solve them simultaneously. To enhance efficiency, we design several non-trivial optimizations that avoid iteratively materializing large dense matrices while maintaining high-quality results. Extensive experiments on diverse attributed hypergraphs and 3 downstream tasks, compared against 11 baselines, show that SAHE consistently outperforms existing methods in embedding quality and is up to orders of magnitude faster.

Problem

• Embedding nodes and hyperedges in attributed hypergraphs effectively
• Addressing scalability challenges in large-scale attributed hypergraph data
• Improving quality and efficiency of existing hypergraph embedding methods

Innovation

• Unifies node and hyperedge embeddings efficiently
• Introduces higher-order similarity measures HMS-N and HMS-E
• Optimizes computations without large dense matrices