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Spectral graph convolutional networks (SGCNs) have been attracting increasing attention in graph representation learning partly due to their interpretability through the prism of the established graph signal processing framework. However, existing SGCNs are limited in implementing graph convolutions with rigid transforms that could not adapt to signals residing on graphs and tasks at hand. In this paper, we propose a novel class of spectral graph convolutional networks that implement graph convolutions 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 for large and varying-size graphs are guaranteed. We further derive a soft-thresholding filtering operation by learning sparse graph representations in terms of the learned wavelets, which improves the scalability and interpretablity, and yield a localized, efficient and scalable spectral graph convolution. 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 SGCNs in terms of accuracy, efficiency and scalability.
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Graph Convolutional Networks (GCNs) have gained great popularity in tackling various analytics tasks on graph and network data. However, some recent studies raise concerns about whether GCNs can optimally integrate node features and topological struc
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Recent years have seen a rise in the development of representational learning methods for graph data. Most of these methods, however, focus on node-level representation learning at various scales (e.g., microscopic, mesoscopic, and macroscopic node e
We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis of GCNs w