Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms and cannot adapt to signals residing on graphs and tasks at hand. In this paper, we propose a novel class of graph neural networks that realizes graph filters with adaptive graph wavelets. Specifically, the adaptive graph wavelets are learned with neural network-parameterized lifting structures, where structure-aware attention-based lifting operations are developed to jointly consider graph structures and node features. We propose to lift based on diffusion wavelets to alleviate the structural information loss induced by partitioning non-bipartite graphs. By design, the locality and sparsity of the resulting wavelet transform as well as the scalability of the lifting structure are guaranteed. We further derive a soft-thresholding filtering operation by learning sparse graph representations in terms of the learned wavelets, yielding a localized, efficient, and scalable wavelet-based graph filters. To ensure that the learned graph representations are invariant to node permutations, a layer is employed at the input of the networks to reorder the nodes according to their local topology information. We evaluate the proposed networks in both node-level and graph-level representation learning tasks on benchmark citation and bioinformatics graph datasets. Extensive experiments demonstrate the superiority of the proposed networks over existing SGNNs in terms of accuracy, efficiency, and scalability.

中文翻译：

---

具有基于提升的自适应图小波的图神经网络

基于谱的图神经网络（SGNN）在图表示学习中引起了越来越多的关注。然而，现有的 SGNN 在实现具有刚性变换的图滤波器方面受到限制，并且不能适应驻留在图上的信号和手头的任务。在本文中，我们提出了一类新颖的图神经网络，它使用自适应图小波实现图滤波器。具体来说，自适应图小波是通过神经网络参数化提升结构来学习的，其中基于结构感知的提升操作被开发以共同考虑图结构和节点特征。我们建议基于扩散小波进行提升，以减轻由划分非二分图引起的结构信息丢失。通过设计，保证了生成的小波变换的局部性和稀疏性以及提升结构的可扩展性。我们通过根据学习的小波学习稀疏图表示，进一步推导出软阈值滤波操作，从而产生局部、高效和可扩展的基于小波的图滤波器。为了确保学习到的图表示不受节点排列的影响，在网络的输入处使用了一个层来根据节点的局部拓扑信息对节点进行重新排序。我们在基准引用和生物信息学图形数据集上评估节点级和图形级表示学习任务中提出的网络。大量实验证明了所提出的网络在准确性、效率和可扩展性方面优于现有的 SGNN。