WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets
Zhirui Yang, Yulan Hu, Sheng Ouyang, Jingyu Liu, Shuqiang Wang, Xibo Ma, Wenhan Wang, Hanjing Su
Abstract
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 Multi-Resolution 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. Our code is available at https://github.com/Bufordyang/WaveNet
BibTeX
@article{Yang_Hu_Ouyang_Liu_Wang_Ma_Wang_Su_Liu_2024, title={WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/28781}, DOI={10.1609/aaai.v38i8.28781}, abstractNote={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 Multi-Resolution 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. Our code is available at https://github.com/Bufordyang/WaveNet}, number={8}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Yang, Zhirui and Hu, Yulan and Ouyang, Sheng and Liu, Jingyu and Wang, Shuqiang and Ma, Xibo and Wang, Wenhan and Su, Hanjing and Liu, Yong}, year={2024}, month={Mar.}, pages={9287-9295} }