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.

翻译：图卷积网络（GCN）是基于图的半监督学习的开创性模型。然而，GCN在稀疏标注图上表现不佳。其两层版本无法有效将标签信息传播至整个图结构（即欠平滑问题），而深层版本则存在过平滑且难以训练的问题（即过平滑问题）。为解决这两个问题，我们提出一种新型图神经网络GND-Nets（图神经扩散网络），该网络在单层中利用顶点的局部和全局邻域信息。浅层网络的使用缓解了过平滑问题，而局部与全局邻域信息的利用则缓解了欠平滑问题。顶点局部和全局邻域信息的利用通过一种名为神经扩散的新型图扩散方法实现，该方法将神经网络融入传统线性与非线性图扩散中。神经网络的引入使得神经扩散能够适应不同数据集。在多种稀疏标注图上的大量实验验证了GND-Nets相较于现有最先进方法的有效性与高效性。