Graph Neural Networks With Convolutional ARMA Filters.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Graph Neural Networks

Background:

• Graph neural networks (GNNs) commonly use polynomial spectral filters for graph convolutions.
• These polynomial filters have limitations in frequency response flexibility and capturing global graph structure.

Purpose of the Study:

• To propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter.
• To enhance GNNs with improved frequency response, noise robustness, and global structure modeling.

Main Methods:

• Developed a graph neural network implementation of the ARMA filter using a recursive and distributed formulation.
• Performed spectral analysis to understand the ARMA layer's filtering effect.
• Evaluated the ARMA layer on four downstream tasks: node classification, graph signal classification, graph classification, and graph regression.

Main Results:

• The proposed ARMA filter offers a more flexible frequency response compared to polynomial filters.
• The ARMA layer demonstrates increased robustness to noise and better capture of global graph structure.
• Experimental results show significant improvements over existing GNNs based on polynomial filters across all evaluated tasks.

Conclusions:

• The ARMA-inspired graph convolutional layer is an efficient and transferable alternative to polynomial filters in GNNs.
• This novel layer enhances GNN performance in various graph-based machine learning tasks.
• The ARMA layer provides a more effective approach for learning from graph-structured data.