Adaptive Expansion for Hypergraph Learning

2025-02-21

AI Summary

Traditional hypergraph unfolding methods employ fixed edge weights, limiting their capacity to preserve higher-order structural information and often resulting in information loss or redundancy. To address this, we propose AdE, an adaptive hypergraph unfolding framework. First, AdE introduces a novel clique-expansion-based adaptive unfolding mechanism that explicitly models higher-order associations. Second, it incorporates a global imitation network to dynamically select representative nodes, thereby enhancing structural representation capability. Third, it designs a distance-aware kernel function to enable topology-adaptive adjustment of edge weights. By integrating adaptive weighted graph unfolding with hypergraph message passing, AdE achieves significant performance gains over classical unfolding models across seven benchmark datasets. Theoretical analysis establishes its superior generalization bound, while extensive experiments validate its effectiveness and robustness.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for 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 learning to rank, online learning, and counterfactual learning for ranking

Abstract

Hypergraph, with its powerful ability to capture higher-order relationships, has gained significant attention recently. Consequently, many hypergraph representation learning methods have emerged to model the complex relationships among hypergraphs. In general, these methods leverage classic expansion methods to convert hypergraphs into weighted or bipartite graphs, and further employ message passing mechanisms to model the complex structures within hypergraphs. However, classical expansion methods are designed in straightforward manners with fixed edge weights, resulting in information loss or redundancy. In light of this, we design a novel clique expansion-based Adaptive Expansion method called AdE to adaptively expand hypergraphs into weighted graphs that preserve the higher-order structure information. Specifically, we introduce a novel Global Simulation Network to select two representative nodes for adaptively symbolizing each hyperedge and connect the rest of the nodes within the same hyperedge to the corresponding selected nodes. Afterward, we design a distance-aware kernel function, dynamically adjusting edge weights to ensure similar nodes within a hyperedge are connected with larger weights. Extensive theoretical justifications and empirical experiments over seven benchmark hypergraph datasets demonstrate that AdE has excellent rationality, generalization, and effectiveness compared to classic expansion models.

Problem

• Adaptive hypergraph expansion
• Preserve higher-order structure
• Dynamic edge weight adjustment

Innovation

• Adaptive Expansion method
• Global Simulation Network
• distance-aware kernel function