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:我们为图中半监督的节点分类提供了一台深图相控内核机器(GCKM) 。 首先, 我们引入了一台不受监督的内核机器, 在一角邻里传播节点特性。 然后, 我们通过Fenchel- Youngng不平等的镜头指定了一台半监督的分类内核机器。 深图相控内核机器是通过堆叠多层浅层内核机器获得的。 在显示未监督和半监督的层分别与一个电子价值问题和一个汇总节点特征的线性系统相对应之后, 我们在双重变量中形成了一种高效的端对端培训算法。 数字实验表明,我们的方法与最先进的光学图形神经网络具有竞争力, 用于共产性和有外溢性的基准数据集。 值得注意的是, GCKM 在极少有标签的情况下, 当有高级性能。