In the existing spectral GNNs, polynomial based methods occupy the mainstream in designing a filter through the Laplacian matrix. However, polynomial combinations factored by the Laplacian matrix naturally have limitations in message passing (e.g., over-smoothing). Furthermore, most existing spectral GNNs are based on polynomial bases, which struggle to capture the high frequency parts of the graph spectral signal. Additionally, we also find that even increasing the polynomial order does not change this situation, which means polynomial based models have a natural deficiency when facing high frequency signals.
To tackle these problems, we propose WaveNet, which aims to effectively capture the high frequency part of the graph spectral signal from the perspective of wavelet bases through reconstructing the message propagation matrix. We utilize MultiResolution Analysis (MRA) to model this question, and our proposed method can reconstruct arbitrary filters theoretically. We also conduct node classification experiments on real world graph benchmarks and achieve superior performance on most datasets.

WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets

Main Track - Data Mining and Knowledge Management

technical paper

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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. 

Zhirui Yang

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WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets

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