Rethinking Spectral Graph Neural Networks With Spatially Adaptive Filtering.

Area of Science:

• Graph Neural Networks
• Machine Learning
• Network Science

Background:

• Spectral graph neural networks (GNNs) are theoretically grounded but lack spatial interpretability.
• Existing GNNs struggle with capturing long-range dependencies and graph heterophily due to polynomial approximations.

Purpose of the Study:

• Investigate the spatial-domain interpretability of spectral GNNs.
• Unveil the connection between spectral filtering and spatial aggregation.
• Propose a novel framework to address limitations in GNNs.

Main Methods:

• Analyzed the theoretical link between spectral filtering and spatial aggregation.
• Developed a spatially adaptive filtering (SAF) framework.
• Conducted extensive experiments on 13 node classification benchmarks.

Main Results:

• Spectral filtering implicitly creates an adapted graph for spatial aggregation.
• The adapted graph exhibits nonlocality and signed edge weights for label consistency.
• The SAF framework effectively models node similarity and dissimilarity globally.

Conclusions:

• Spectral GNNs have an interpretable spatial role beyond fixed-order polynomials.
• The SAF framework significantly improves GNN performance on node classification tasks.
• The findings offer new perspectives on designing spectral graph filters.