Shape-aware Graph Spectral Learning
Junjie Xu, Enyan Dai, Dongsheng Luo, Xiang Zhang, Suhang Wang
TL;DR
This paper introduces a shape-aware spectral learning method for Graph Neural Networks that leverages graph homophily levels to learn spectral filters with desired frequency characteristics, improving performance across diverse graph types.
Contribution
It provides a theoretical and empirical analysis of the relationship between spectral importance and homophily, and proposes a Newton Interpolation-based regularization to shape spectral filters.
Findings
Positive correlation between low-frequency importance and homophily.
Negative correlation between high-frequency importance and homophily.
NewtonNet achieves superior performance on various datasets.
Abstract
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)…
Peer Reviews
Decision·Submitted to ICLR 2024
The paper is well-written and provides the relevant message of the importance of homophily in learning of spectral graph filters coherently. Theoretical statements with elementary numerical analysis in Section 3 is well done.
In practice, incorporating homophily information might offer the most significant benefits when the datasets are of limited size. For sufficiently large datasets, the graph filters will be fine-tuned automatically according to the graph homophily level.
S1. The theoretical part is contributive and justified with well-designed experiments. S2. The idea of controlling the shape of a polynomial filter via Newton nodes is interesting. S3. The paper is well-organized. S4. The code is accessible.
> W1. On the choice of K. First, In the second line under Eq.7, the authors write that they set K=4 in this paper. According to Fig.2 and the description of experimental settings in Appendix D.4, you want to write K=5, right? Then, in Appendix E.1, the authors conduct a sensitivity analysis on K, and find that NewtonNet's performances on the Cora and Chameleon datasets peak at K=5. Such an analysis is weird since **the accuracies on test datasets are in fact used as prior knowledge**. A valid
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Taxonomy
TopicsAdvanced Graph Neural Networks · Traffic Prediction and Management Techniques
MethodsALIGN