We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. First, we introduce an unsupervised kernel machine propagating the node features in a one-hop neighbourhood. Then, we specify a semi-supervised classification kernel machine through the lens of the Fenchel-Young inequality. The deep graph convolutional kernel machine is obtained by stacking multiple shallow kernel machines. After showing that unsupervised and semi-supervised layer corresponds to an eigenvalue problem and a linear system on the aggregated node features, respectively, we derive an efficient end-to-end training algorithm in the dual variables. Numerical experiments demonstrate that our approach is competitive with state-of-the-art graph neural networks for homophilious and heterophilious benchmark datasets. Notably, GCKM achieves superior performance when very few labels are available.

翻译：我们提出了一种深度图卷积核机器（GCKM），用于图中的半监督节点分类。首先，我们引入了一种无监督核机器，可在单跳邻域内传播节点特征。随后，通过芬切尔-杨不等式（Fenchel-Young inequality）的视角，我们指定了一个半监督分类核机器。通过堆叠多个浅层核机器，得到了深度图卷积核机器。在证明无监督层和半监督层分别对应于聚合节点特征的特征值问题和线性系统之后，我们推导出一种高效的端到端对偶变量训练算法。数值实验表明，我们的方法在同质性和异质性基准数据集上均与最先进的图神经网络具有竞争力。值得注意的是，当可用标签非常少时，GCKM实现了优越的性能。