LAUSR

We present a spatial graph convolution (GC) to classify signals on a graph. Existing GC methods are limited in using the structural information in the feature space. Furthermore, GCs only aggregate features from one-hop neighboring nodes to the target node in their single step. In this paper, we propose two methods to improve the performance of GCs: 1) Utilizing structural information in the feature space, and 2) exploiting the multi-hop information in one GC step. In the first method, we define three structural features in the feature space: feature angle, feature distance, and relational embedding. The second method aggregates the node-wise features of multi-hop neighbors in a GC. Both methods can be simultaneously used. We also propose graph neural networks (GNNs) integrating the proposed GC for classifying nodes in 3D point clouds and citation networks. In experiments, the proposed GNNs exhibited a higher classification accuracy than existing methods.