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arxiv_ml 90% Match Research Paper ML Researchers,Data Scientists,Graph Theory Experts 1 week ago

Higher-Order Regularization Learning on Hypergraphs

graph-neural-networks › graph-learning
📄 Abstract

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.
Authors (3)
Adrien Weihs
Andrea Bertozzi
Matthew Thorpe
Submitted
October 30, 2025
arXiv Category
cs.LG
arXiv PDF

Key Contributions

Extends the theoretical foundation of Higher-Order Hypergraph Learning (HOHL) by proving the consistency of a truncated version and deriving explicit convergence rates for its use as a regularizer in supervised learning. Demonstrates strong empirical performance in active learning and diverse datasets, highlighting HOHL's versatility.

Business Value

Improves the robustness and applicability of hypergraph-based learning methods, potentially leading to more accurate predictions and better data utilization in complex relational data scenarios.

Paper Metadata

Innovation Type

Theoretical and Algorithmic

Deployment Feasibility

Moderate, requires specialized hypergraph data structures and understanding of HOHL principles.

Limitations Addressed

Prior work's focus on asymptotic consistency in geometric settings; provides theoretical guarantees for truncated HOHL and its application in broader learning scenarios.

Technical Tags

Higher-Order Hypergraph Learning (HOHL)hypergraph regularizationLaplacian matricesconsistency analysisconvergence ratesactive learningsupervised learninggeometric settings

Research Topics

Hypergraph LearningMachine Learning TheoryRegularization TechniquesGraph Signal Processing

Methods & Architectures

Higher-Order Hypergraph Learning (HOHL)Truncated HOHLAsymptotic consistency analysisConvergence rate derivation

Applications & Tasks

Machine Learning Data Analysis Learning on HypergraphsRegularizationData Scarcity Hypergraph regularizationSupervised learningActive learning

Related Fields

Graph TheoryMachine LearningSignal ProcessingData Mining

Keywords

hypergraph learninghigher-order regularizationLaplacianconsistencyconvergenceactive learningsupervised learninggraph theorymachine learningdata analysis

Academic Context

#Hypergraph Learning#Machine Learning Theory#Regularization Techniques#Graph Signal Processing

Commercial Potential

Potential Products
Advanced graph-based analytics toolsSpecialized machine learning libraries for hypergraphs
Target Industries
Social NetworksBioinformaticsRecommendation SystemsCybersecurity
Use Case Examples
Modeling complex relationships in social networksAnalyzing biological interaction networksImproving recommendation systems with higher-order features
Competitive Edge
Provides a more theoretically sound and empirically validated approach to hypergraph regularization, extending its applicability beyond specific geometric assumptions.
Market Opportunity
Niche but growing, related to graph analytics and complex systems modeling.
Revenue Models
Integration into specialized data analysis platformsconsulting services.

Resource Requirements

Compute Needs
Moderate, depends on hypergraph size and complexity.
Data Requirements
Hypergraph-structured data.
Deployment Constraints
Requires efficient hypergraph representation and manipulation libraries.
Scalability
Scalability depends on the efficiency of hypergraph operations and the chosen HOHL variant.

Production Readiness

Maturity Level

Research

Time to Market

1-3 years for practical library development and adoption.

Patent Potential

Low to moderate, primarily theoretical contributions.

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