A Piece-Wise Polynomial Filtering Approach for Graph Neural Networks

Lingam, Vijay; Sharma, Manan; Ekbote, Chanakya; Ragesh, Rahul; Iyer, Arun; Sellamanickam, Sundararajan

doi:10.1007/978-3-031-26390-3_25

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…2 can be considered as the homogeneous spectral filtering, where all nodes share the identical coefficient ŝ𝑛 equally operated on their basis signals, i.e., all elements in u 𝑛 , for feature transformation. It seems reasonable as one can learn arbitrary ŝ𝑛 with a polynomial graph filter [37], which formally requires high-degree polynomials and reaching high-order node neighborhood [9,20,28]. However, aggregating/passing information across a long path via L𝑘 X with 𝑘 → ∞ is prone to cause overfitting to noises and/or over-squashing problem [2].…”

Section: Motivationsmentioning

confidence: 99%

“…Existing efforts either design or learn the polynomial coefficients to simulate different types of filters including low, band, and/or high-pass. Despite their success, high degree polynomials are necessary as typically required by their expressive power [9,20,28] so as to reach high-order neighborhoods. Nevertheless, most spectral GNNs would fail practically due to the overfitting and/or over-squashing problem [2,9,42].…”

Section: Introductionmentioning

confidence: 99%

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Graph Neural Networks with Diverse Spectral Filtering

Guo

Huang

et al. 2023

Proceedings of the ACM Web Conference 2023

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Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph machine learning, with polynomial filters applied for graph convolutions, where all nodes share the identical filter weights to mine their local contexts. Despite the success, existing spectral GNNs usually fail to deal with complex networks (e.g., WWW) due to such homogeneous spectral filtering setting that ignores the regional heterogeneity as typically seen in real-world networks. To tackle this issue, we propose a novel diverse spectral filtering (DSF) framework, which automatically learns node-specific filter weights to exploit the varying local structure properly. Particularly, the diverse filter weights consist of two components -A global one shared among all nodes, and a local one that varies along network edges to reflect node difference arising from distinct graph parts -to balance between local and global information. As such, not only can the global graph characteristics be captured, but also the diverse local patterns can be mined with awareness of different node positions. Interestingly, we formulate a novel optimization problem to assist in learning diverse filters, which also enables us to enhance any spectral GNNs with our DSF framework. We showcase the proposed framework on three state-of-the-arts including GPR-GNN, BernNet, and JacobiConv. Extensive experiments over 10 benchmark datasets demonstrate that our framework can consistently boost model performance by up to 4.92% in node classification tasks, producing diverse filters with enhanced interpretability. Code is available at https://github.com/jingweio/DSF. CCS CONCEPTS• Computing methodologies → Machine learning.

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Section: Motivationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Graph Neural Networks with Diverse Spectral Filtering

Guo

Huang

et al. 2023

Proceedings of the ACM Web Conference 2023

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“…We also report performance using the restructuring methods GDC (Klicpera, Weißenberger, and Günnemann 2019). Five recent GNNs that target heterophilic graphs are also listed as baselines: GPRGNN (Chien et al 2021), H 2 GCN (Zhu et al 2020), Geom-GCN (Pei et al 2020), BernNet (He et al 2021) and PPGNN (Lingam et al 2021). We evaluate on four real-world graphs: TEXAS, CORNELL, CHAMELEON and SQUIRREL (Rozemberczki, Allen, and Sarkar 2021), as well as synthetic graphs of controlled homophily.…”

Section: A New Homophily Measurementioning

confidence: 99%

Restructuring Graph for Higher Homophily via Adaptive Spectral Clustering

Kim

Wang

2023

AAAI

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While a growing body of literature has been studying new Graph Neural Networks (GNNs) that work on both homophilic and heterophilic graphs, little has been done on adapting classical GNNs to less-homophilic graphs. Although the ability to handle less-homophilic graphs is restricted, classical GNNs still stand out in several nice properties such as efficiency, simplicity, and explainability. In this work, we propose a novel graph restructuring method that can be integrated into any type of GNNs, including classical GNNs, to leverage the benefits of existing GNNs while alleviating their limitations. Our contribution is threefold: a) learning the weight of pseudo-eigenvectors for an adaptive spectral clustering that aligns well with known node labels, b) proposing a new density-aware homophilic metric that is robust to label imbalance, and c) reconstructing the adjacency matrix based on the result of adaptive spectral clustering to maximize the homophilic scores. The experimental results show that our graph restructuring method can significantly boost the performance of six classical GNNs by an average of 25% on less-homophilic graphs. The boosted performance is comparable to state-of-the-art methods.

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Leveraging Free Labels to Power up Heterophilic Graph Learning in Weakly-Supervised Settings: An Empirical Study

Wu,

Wang

et al. 2023

Lecture Notes in Computer Science

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A Piece-Wise Polynomial Filtering Approach for Graph Neural Networks

Cited by 4 publications

References 20 publications

Graph Neural Networks with Diverse Spectral Filtering

Graph Neural Networks with Diverse Spectral Filtering

Restructuring Graph for Higher Homophily via Adaptive Spectral Clustering

Leveraging Free Labels to Power up Heterophilic Graph Learning in Weakly-Supervised Settings: An Empirical Study

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