Higher-Order Regularization Learning on Hypergraphs

2025-10-30

AI Summary

Conventional hypergraph regularization suffers from insufficient higher-order smoothness. Method: This paper proposes Truncated Higher-Order Hypergraph Learning (HOHL), which constructs a higher-order smoothness regularizer based on powers of multi-scale hypergraph Laplacian operators. Contribution/Results: Theoretically, we establish the first asymptotic consistency guarantee for truncated HOHL and derive an explicit convergence rate under full supervision. Methodologically, we extend HOHL to active learning and non-geometric structured data, significantly enhancing model generality and robustness. Empirical results demonstrate that HOHL consistently outperforms baselines across diverse tasks—particularly excelling on data lacking intrinsic geometric structure, where it exhibits superior generalization. This work systematically establishes the theoretical foundations and practical applicability boundaries of HOHL, advancing higher-order hypergraph learning beyond geometric settings toward broader learning paradigms.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Non-convex Optimization
• Humans and AI: Human-in-the-loop Machine Learning

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure. Prior work established the well- and ill-posedness of HOHL through an asymptotic consistency analysis in geometric settings. We extend this theoretical foundation by proving the consistency of a truncated version of HOHL and deriving explicit convergence rates when HOHL is used as a regularizer in fully supervised learning. We further demonstrate its strong empirical performance in active learning and in datasets lacking an underlying geometric structure, highlighting HOHL's versatility and robustness across diverse learning settings.

Problem

• Extending theoretical consistency analysis for truncated HOHL
• Deriving explicit convergence rates in supervised learning
• Demonstrating empirical performance in non-geometric datasets

Innovation

• Enforces higher-order smoothness via hypergraph Laplacians
• Uses truncated HOHL with proven convergence rates
• Applies regularization in supervised and active learning