  Graph Convolutional Networks (GCN) is a pioneering model for graph-based
semi-supervised learning. However, GCN does not perform well on
sparsely-labeled graphs. Its two-layer version cannot effectively propagate the
label information to the whole graph structure (i.e., the under-smoothing
problem) while its deep version over-smoothens and is hard to train (i.e., the
over-smoothing problem). To solve these two issues, we propose a new graph
neural network called GND-Nets (for Graph Neural Diffusion Networks) that
exploits the local and global neighborhood information of a vertex in a single
layer. Exploiting the shallow network mitigates the over-smoothing problem
while exploiting the local and global neighborhood information mitigates the
under-smoothing problem. The utilization of the local and global neighborhood
information of a vertex is achieved by a new graph diffusion method called
neural diffusions, which integrate neural networks into the conventional linear
and nonlinear graph diffusions. The adoption of neural networks makes neural
diffusions adaptable to different datasets. Extensive experiments on various
sparsely-labeled graphs verify the effectiveness and efficiency of GND-Nets
compared to state-of-the-art approaches.
