An example is the graph convolutional kernel support vector machine (GCKSVM) for node classification, for which we analyze the generalization error bound and discuss the impact of the graph structure.

Graph convolutional networks (GCN) with one or two hidden layers have been widely used in handling graph data that are prevalent in various disciplines. Many studies showed that the gain of making GCNs deeper is tiny or even negative. This implies that the complexity of graph data is often limited and shallow models are often sufficient to extract expressive features for various tasks such as node classification. Therefore, in this work, we present a framework called graph convolutional kernel machine (GCKM) for graph-based machine learning. GCKMs are built upon kernel functions integrated with graph convolution.

Graph convolutional networks (GCN) with one or two hidden layers have been widely used in handling graph data that are prevalent in various disciplines. Many studies showed that the gain of making GCNs deeper is tiny or even negative. This implies that the complexity of graph data is often limited and shallow models are often sufficient to extract expressive features for various tasks such as node classification. Therefore, in this work, we present a framework called graph convolutional kernel machine (GCKM) for graph-based machine learning. GCKMs are built upon kernel functions integrated with graph convolution.

We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. The method is built of two main types of blocks: (i) We introduce unsupervised kernel machine layers propagating the node features in a one-hop neighborhood, using implicit node feature mappings. (ii) We specify a semi-supervised classification kernel machine through the lens of the Fenchel-Young inequality. We derive an effective initialization scheme and efficient end-to-end training algorithm in the dual variables for the full architecture. The main idea underlying GCKM is that, because of the unsupervised core, the final model can achieve higher performance in semi-supervised node classification when few labels are available for training. Experimental results demonstrate the effectiveness of the proposed framework.