Graph Wavelet Neural Network

By Bingbing Xu, Huawei Shen, Qi Cao, Yunqi Qiu, Xueqi Cheng. International Conference on Learning Representations, 2019

397 citations recorded by the source corpus.

We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform. Different from graph Fourier transform, graph wavelet transform can be obtained via a fast algorithm without requiring matrix eigendecomposition with high computational cost. Moreover, graph wavelets are sparse and localized in vertex domain, offering high efficiency and good interpretability for graph convolution. The proposed GWNN significantly outperforms previous spectral graph CNNs in the task of graph-based semi-supervised classification on three benchmark datasets: Cora, Citeseer and Pubmed.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9f91568d8ec72c417d9146a551b61e69ccf1f848

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In Artificial Intelligence

In Computer Vision and Pattern Recognition

In Statistical and Nonlinear Physics

Citations in the corpus

BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation (2021, background): “Recent studies suggest that many popular GNNs operate as polynomial graph spectral filters [7, 13, 5, 16, 2, 35].”
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks (2021, methodology): “We follow the same experimental setting and evaluation procedure described in Xu et al. (2019b).”
Graph convolutional networks: a comprehensive review (2019, background): “propose to use the spectral wavelet transform on graphs, such that the consequent model can vary different scales of graphs to be captured [44].”
Rethinking Graph Neural Networks for Anomaly Detection (2022, methodology): “We discuss the differences between the proposed BWGNN and other related wavelet GNNs. Heat kernel-based methods (Xu et al., 2019a; Donnat et al., 2018; Li et al., 2021) do not essentially satisfy Hammond’s graph wavelet theory (Hammond et al., 2011) because they are not band-pass.”
Principal Neighbourhood Aggregation for Graph Nets (2020, methodology): “Finally, we detail the design of graph convolutional layers which leverage the proposed Principal Neighbourhood Aggregation.”
DeeperGCN: All You Need to Train Deeper GCNs (2020, methodology): “The methods include GCN [Kipf and Welling, 2016], GraphSAGE [Hamilton et al., 2017], GIN [Xu et al., 2019b], GIN with virtual nodes, GaAN [Zhang et al., 2018], and GatedGCN [Bresson and Laurent, 2018].”
Simple and Deep Graph Convolutional Networks (2020, methodology): “(Xu et al., 2019) uses the graph wavelet basis instead of the Fourier basis to improve sparseness and locality.”
Beyond Low-frequency Information in Graph Convolutional Networks (2021, methodology): “…GCN (Kipf and Welling 2017), ChebNet (Defferrard, Bresson, and Vandergheynst 2016) and GWNN (Xu et al. 2019b); Spatial-based methods, i.e., GIN (Xu et al. 2019c), GAT (Velickovic et al. 2018), MoNet (Monti et al. 2017), GraphSAGE (Hamilton, Ying, and Leskovec 2017) and APPNP (Klicpera,…”
Deep Learning on Graphs: A Survey (2018, neutral): “Graph wavelet neural network (GWNN) [45] was further proposed to replace the Fourier transform in spectral filters by the graph wavelet transform by rewriting Eq.”
Graph Transformer Networks (2019, background): “They are categorized into two approaches: spectral [5, 9, 15, 19, 22, 38] and non-spectral methods [7, 12, 14, 26, 29, 33].”