  We introduce a family of multilayer graph kernels and establish new links
between graph convolutional neural networks and kernel methods. Our approach
generalizes convolutional kernel networks to graph-structured data, by
representing graphs as a sequence of kernel feature maps, where each node
carries information about local graph substructures. On the one hand, the
kernel point of view offers an unsupervised, expressive, and easy-to-regularize
data representation, which is useful when limited samples are available. On the
other hand, our model can also be trained end-to-end on large-scale data,
leading to new types of graph convolutional neural networks. We show that our
method achieves competitive performance on several graph classification
benchmarks, while offering simple model interpretation. Our code is freely
available at https://github.com/claying/GCKN.
