Graph Neural Networks With Lifting-based Adaptive Graph Wavelets

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