T-HyperGNNs: Hypergraph Neural Networks via Tensor Representations.

Area of Science:

• Machine Learning
• Graph Neural Networks
• Hypergraph Analysis

Background:

• Hypergraph Neural Networks (HyperGNNs) are effective for data with complex relationships.
• Existing HyperGNNs often rely on matrix representations and have limited exploration of high-dimensional descriptors and joint node interactions.
• There is a need for advanced HyperGNN models that preserve intrinsic high-order network structures.

Purpose of the Study:

• To propose a novel Tensor-Hypergraph Neural Network (T-HyperGNN) framework.
• To incorporate high-dimensional tensor descriptors and model joint node interactions via Cross-Node Interactions (CNIs).
• To develop efficient spectral and spatial convolution methods for hypergraphs.

Main Methods:

• Developed T-HyperGNN framework with T-spectral convolution, T-spatial convolution, and T-message-passing HyperGNNs (T-MPHN).
• Utilized t-product algebra for spectral convolution and localized it for spatial efficiency.
• Introduced a compressed adjacency tensor representation for efficient tensor-message-passing.

Main Results:

• T-HyperGNNs successfully preserve high-order network structures without hypergraph reduction.
• The Cross-Node Interaction (CNI) layer effectively models joint node effects.
• Demonstrated superior performance across various real-world hypergraph datasets.

Conclusions:

• T-HyperGNNs offer a powerful new approach for hypergraph representation learning.
• The tensor-based framework enhances the ability to model complex relational data.
• The proposed methods provide significant improvements over existing state-of-the-art HyperGNNs.