Kernelized Hypergraph Neural Networks.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Data Science

Background:

• Hypergraph Neural Networks (HGNNs) are crucial for learning from high-order structural data.
• Current HGNN methods often rely on simple aggregations, limiting non-linear modeling and distribution sensitivity.
• Existing kernel-based approaches in GNNs/CNNs have limitations in capturing high-order correlations and computational stability.

Purpose of the Study:

• To introduce Kernelized Hypergraph Neural Networks (KHGNN) and Half-Kernelized Hypergraph Neural Networks (H-KHGNN) for enhanced representation learning.
• To develop methods that overcome the limitations of existing HGNNs in non-linear modeling and computational stability.
• To provide a mathematically grounded approach for comprehensive feature extraction in hypergraphs.

Main Methods:

• KHGNN employs a kernelized aggregation strategy, blending mean-based and max-based functions with learnable parameters.
• H-KHGNN selectively uses non-linear aggregation during message passing to reduce complexity and prevent overfitting in simpler hypergraphs.
• Theoretical analysis provides a bounded gradient for kernelized aggregation, ensuring computational stability.

Main Results:

• KHGNN and H-KHGNN demonstrate superior performance compared to state-of-the-art models on 10 diverse graph/hypergraph datasets.
• Ablation studies confirm the effectiveness of the proposed methods in representation learning.
• The developed methods exhibit significant computational stability during training and inference.

Conclusions:

• KHGNN and H-KHGNN represent a significant advancement in hypergraph representation learning.
• The kernelized aggregation strategy offers a robust and adaptive approach to capturing both semantic and structural information.
• These novel HGNN variants provide stable and effective solutions for complex, high-order data analysis.