Shape-aware Graph Spectral Learning
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917672901410816 |
|---|---|
| author | Xu, Junjie Dai, Enyan Luo, Dongsheng Zhang, Xiang Wang, Suhang |
| author_facet | Xu, Junjie Dai, Enyan Luo, Dongsheng Zhang, Xiang Wang, Suhang |
| contents | Spectral Graph Neural Networks (GNNs) are gaining attention for their ability to surpass the limitations of message-passing GNNs. They rely on supervision from downstream tasks to learn spectral filters that capture the graph signal's useful frequency information. However, some works empirically show that the preferred graph frequency is related to the graph homophily level. This relationship between graph frequency and graphs with homophily/heterophily has not been systematically analyzed and considered in existing spectral GNNs. To mitigate this gap, we conduct theoretical and empirical analyses revealing a positive correlation between low-frequency importance and the homophily ratio, and a negative correlation between high-frequency importance and the homophily ratio. Motivated by this, we propose shape-aware regularization on a Newton Interpolation-based spectral filter that can (i) learn an arbitrary polynomial spectral filter and (ii) incorporate prior knowledge about the desired shape of the corresponding homophily level. Comprehensive experiments demonstrate that NewtonNet can achieve graph spectral filters with desired shapes and superior performance on both homophilous and heterophilous datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10064 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shape-aware Graph Spectral Learning Xu, Junjie Dai, Enyan Luo, Dongsheng Zhang, Xiang Wang, Suhang Machine Learning Artificial Intelligence Spectral Graph Neural Networks (GNNs) are gaining attention for their ability to surpass the limitations of message-passing GNNs. They rely on supervision from downstream tasks to learn spectral filters that capture the graph signal's useful frequency information. However, some works empirically show that the preferred graph frequency is related to the graph homophily level. This relationship between graph frequency and graphs with homophily/heterophily has not been systematically analyzed and considered in existing spectral GNNs. To mitigate this gap, we conduct theoretical and empirical analyses revealing a positive correlation between low-frequency importance and the homophily ratio, and a negative correlation between high-frequency importance and the homophily ratio. Motivated by this, we propose shape-aware regularization on a Newton Interpolation-based spectral filter that can (i) learn an arbitrary polynomial spectral filter and (ii) incorporate prior knowledge about the desired shape of the corresponding homophily level. Comprehensive experiments demonstrate that NewtonNet can achieve graph spectral filters with desired shapes and superior performance on both homophilous and heterophilous datasets. |
| title | Shape-aware Graph Spectral Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2310.10064 |