[Paper Review] Graph Wavelet Neural Network

Bingbing Xu, Huawei Shen+3 more|arXiv (Cornell University)|Apr 12, 2019

Advanced Graph Neural NetworksComputer Science78 citations

TL;DR

GWNN replaces graph Fourier-based convolution with graph wavelet transform, enabling efficient, sparse, and localized graph convolutions that improve semi-supervised node classification on Cora, Citeseer, and Pubmed.

ABSTRACT

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.

Motivation & Objective

• Motivate graph convolution on non-Euclidean data and address limitations of graph Fourier-based methods.
• Introduce graph wavelet transform as a basis for graph convolution.
• Develop an efficient GWNN architecture with reduced parameter complexity.
• Demonstrate GWNN’s effectiveness on standard semi-supervised node classification benchmarks (Cora, Citeseer, Pubmed).

Proposed method

• Define graph wavelet transform using Laplacian eigenvectors with the scaling matrix G_s and wavelets psi_s.
• Formulate graph convolution as x *G y = psi_s ((psi_s^{-1} y) ⊙ (psi_s^{-1} x)).
• Propose an efficient two-layer GWNN with a parameter-efficient separation of feature transformation (X^m' = X^m W) from graph convolution.
• Use a diagonal filter matrix F^m in the spectral domain and a non-linear activation h (ReLU/softmax for outputs).
• Train with cross-entropy loss over labeled nodes and optimize via gradient descent.
• Show that sparsity and locality of psi_s and psi_s^{-1} yield efficient, interpretable convolutions.

Experimental results

Research questions

• RQ1 Does GWNN outperform traditional spectral CNNs on standard graph-based semi-supervised classification datasets?
• RQ2 What is the impact of detaching feature transformation from graph convolution on parameter efficiency and accuracy?
• RQ3 How do the sparsity and locality properties of graph wavelets affect model performance and interpretability?

Key findings

• GWNN consistently outperforms previous spectral CNNs on Cora, Citeseer, and Pubmed.
• GWNN achieves 82.8% (Cora), 71.7% (Citeseer), and 79.1% (Pubmed) accuracy in the reported setup.
• Replacing graph Fourier transform with graph wavelet transform yields about 10% accuracy gains on Cora and Citeseer, and about 5% on Pubmed compared to Spectral CNN.
• Detaching feature transformation from convolution reduces parameter counts (e.g., ChebyNet baseline: 46,080–178,032 parameters vs. Detaching-ChebyNet: 23,048–59,348) and can improve accuracy, notably on Pubmed (78.6% vs 74.4%).
• GWNN’s sparsity (e.g., 2.8% transform density vs 99.1% for Fourier) and locality of wavelets contribute to efficiency and interpretability.