  In this paper, we propose a spatial graph convolution (GC) to classify
signals on a graph. Existing GC methods are limited to using the structural
information in the feature space. Additionally, the single step of GCs only
uses features on the one-hop neighboring nodes from the target node. 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.
