A Simple Yet Effective Framelet-Based Graph Neural Network for Directed Graphs

Zou, Chunya; Han, Andi; Lin, Lequan; Li, Ming; Gao, Junbin

doi:10.1109/tai.2023.3316628

Cited by 2 publications

(3 citation statements)

References 27 publications

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“…The recent studies show that framelet can naturally decompose the graph signal and re-aggregate them effectively, achieving a significant result on graph noise reduction [62] with the use of a double term regularizer on the framelet coefficients. Combing with singular value decomposition (SVD), the framelets have been made applicable to directed graphs [69].…”

Section: Graph Frameletsmentioning

confidence: 99%

“…Among various spectral-based GNNs, the graph framelets GCN [61], which is constructed on a type of wavelet frame analogized from the identical concept defined on manifold [15], further separates the input signal by predefined low-pass and high-pass filtering functions and resulting a convolution-type model as in the studies [9,60,61]. The graph framelet shows great flexibility in terms of controlling both low and high-frequency information with robustness to noise and thus in general possesses high prediction power in multiple graph learning tasks [9,56,60,62,63,69].…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, one may be interested in identifying whether the advantage of deploying p-Laplacian in GNN still remains in graph framelet or what is the exact functionality of p-Laplacian interacting with the feature representations generated both low and high pass framelet domains. In addition, as graph framelets have shown great potential in terms of the graph noise reduction [56,61,69], whether the inclusion of p-Laplacian regularizer could enhance/ dilute such power remains unclear. These research gaps inspire us to incorporate p-Laplacian into graph framelets and explore further for the underlying relationship between them.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Enhancing framelet GCNs with generalized p-Laplacian regularization

Shao,

Shi,

Han

et al. 2023

Int. J. Mach. Learn. & Cyber.

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Graph neural networks (GNNs) have achieved remarkable results for various graph learning tasks. However, one of the recent challenges for GNNs is to adapt to different types of graph inputs, such as heterophilic graph datasets in which linked nodes are more likely to contain a different class of labels and features. Accordingly, an ideal GNN model should adaptively accommodate all types of graph datasets with different labeling distributions. In this paper, we tackle this challenge by proposing a regularization framework on graph framelet with the regularizer induced from graph p-Laplacian. By adjusting the value of p, the p-Laplacian based regularizer restricts the solution space of graph framelet into the desirable region based on the graph homophilic features. We propose an algorithm to effectively solve a more generalized regularization problem and prove that the algorithm imposes a (p-Laplacian based) spectral convolution and diagonal scaling operation to the framelet filtered node features. Furthermore, we analyze the denoising power of the proposed model and compare it with the predefined framelet denoising regularizer. Finally, we conduct empirical studies to show the prediction power of the proposed model in both homophily undirect and heterophily direct graphs with and without noises. Our proposed model shows significant improvements compared to multiple baselines, and this suggests the effectiveness of combining graph framelet and p-Laplacian.

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Section: Graph Frameletsmentioning

confidence: 99%