Rotation-Equivariant Graph Convolutional Networks for Spherical Data Via Global-Local Attention.

Graph convolutional networks (GCNs) are widely adopted for spherical data processing, striking a balance between rotation equivariance and computation efficiency. However, current GCN-based approaches either apply radial filters with a fixed convolution kernel, or adopt attention schemes to learn a variable kernel based only on node features, which lack expressiveness and may suffer over-smoothing problem. To address this, in this paper, we propose a global-local attention-based spherical graph convolution (GlasGC) for spherical data representation. Specifically, the designed graph convolution includes a structure-enhanced local attention module to estimate the structure correlation efficiently based on topological characteristics of the given spherical graph. The structure correlation is then incorporated with the feature correlation to form the local attention that determines importance of a neighbor node to the center node. We also design a global attention module to obtain the importance scores of different nodes based on both node features and graph topology, which acts as a message-passing enhancer for informative nodes and can relieve the over-smoothing problem. Based on our proposed GlasGC, we design specific GlasGCNs for classification and semantic segmentation of spherical data. Empirical evaluations on these tasks demonstrate that our proposed GlasGCNs can generally achieve better classification and segmentation performance.