An Adaptive Neighborhood-Resonated Graph Convolution Network for Undirected Weighted Graph Representation.

Area of Science:

• Graph representation learning
• Machine learning on graphs
• Network science

Background:

• Undirected weighted graphs (UWGs) are crucial in many applications.
• Graph Convolutional Networks (GCNs) are common for UWG representation learning.
• Existing GCNs suffer from information loss by only considering local neighborhoods.

Purpose of the Study:

• Propose an Adaptive Neighborhood-Resonated Graph Convolution Network (ANR-GCN).
• Enhance representation learning capability for UWGs.
• Improve performance on tasks like missing edge detection.

Main Methods:

• Incorporate link weights into embedding propagation for interaction strength.
• Implement neighborhood-regularization (NR) for node-neighborhood resonance.
• Utilize attention mechanisms to diversify NR effects.

Main Results:

• Theoretically guaranteed representation learning ability via bounded generalization error and uniform stability.
• ANR-GCN significantly outperforms state-of-the-art GCNs on four UWG datasets.
• Demonstrated superior performance in missing edge detection tasks.

Conclusions:

• The proposed ANR-GCN effectively addresses information loss in traditional GCNs.
• ANR-GCN shows significant improvements in learning complex graph topologies.
• The model offers a robust solution for UWG representation learning and related applications.