  Graph kernels are kernel methods measuring graph similarity and serve as a
standard tool for graph classification. However, the use of kernel methods for
node classification, which is a related problem to graph representation
learning, is still ill-posed and the state-of-the-art methods are heavily based
on heuristics. Here, we present a novel theoretical kernel-based framework for
node classification that can bridge the gap between these two representation
learning problems on graphs. Our approach is motivated by graph kernel
methodology but extended to learn the node representations capturing the
structural information in a graph. We theoretically show that our formulation
is as powerful as any positive semidefinite kernels. To efficiently learn the
kernel, we propose a novel mechanism for node feature aggregation and a
data-driven similarity metric employed during the training phase. More
importantly, our framework is flexible and complementary to other graph-based
deep learning models, e.g., Graph Convolutional Networks (GCNs). We empirically
evaluate our approach on a number of standard node classification benchmarks,
and demonstrate that our model sets the new state of the art.
