  This paper studies semi-supervised graph classification, which is an
important problem with various applications in social network analysis and
bioinformatics. This problem is typically solved by using graph neural networks
(GNNs), which yet rely on a large number of labeled graphs for training and are
unable to leverage unlabeled graphs. We address the limitations by proposing
the Kernel-based Graph Neural Network (KGNN). A KGNN consists of a GNN-based
network as well as a kernel-based network parameterized by a memory network.
The GNN-based network performs classification through learning graph
representations to implicitly capture the similarity between query graphs and
labeled graphs, while the kernel-based network uses graph kernels to explicitly
compare each query graph with all the labeled graphs stored in a memory for
prediction. The two networks are motivated from complementary perspectives, and
thus combing them allows KGNN to use labeled graphs more effectively. We
jointly train the two networks by maximizing their agreement on unlabeled
graphs via posterior regularization, so that the unlabeled graphs serve as a
bridge to let both networks mutually enhance each other. Experiments on a range
of well-known benchmark datasets demonstrate that KGNN achieves impressive
performance over competitive baselines.
