Graph Deformer Network

Convolution learning on graphs draws increasing attention recently due to its potential applications to a large amount of irregular data. Most graph convolution methods leverage the plain summation/average aggregation to avoid the discrepancy of responses from isomorphic graphs. However, such an extreme collapsing way would result in a structural loss and signal entanglement of nodes, which further cause the degradation of the learning ability. In this paper, we propose a simple yet effective Graph Deformer Network (GDN) to fulfill anisotropic convolution filtering on graphs, analogous to the standard convolution operation on images. Local neighborhood subgraphs (acting like receptive fields) with different structures are deformed into a unified virtual space, coordinated by several anchor nodes. In the deformation process, we transfer components of nodes therein into affinitive anchors by learning their correlations, and build a multi-granularity feature space calibrated with anchors. Anisotropic convolutional kernels can be further performed over the anchor-coordinated space to well encode local variations of receptive fields. By parameterizing anchors and stacking coarsening layers, we build a graph deformer network in an end-to-end fashion. Theoretical analysis indicates its connection to previous work and shows the promising property of graph isomorphism testing. Extensive experiments on widely-used datasets validate the effectiveness of GDN in graph and node classifications.