  A novel kernel-based support vector machine (SVM) for graph classification is
proposed. The SVM feature space mapping consists of a sequence of graph
convolutional layers, which generates a vector space representation for each
vertex, followed by a pooling layer which generates a reproducing kernel
Hilbert space (RKHS) representation for the graph. The use of a RKHS offers the
ability to implicitly operate in this space using a kernel function without the
computational complexity of explicitly mapping into it. The proposed model is
trained in a supervised end-to-end manner whereby the convolutional layers, the
kernel function and SVM parameters are jointly optimized with respect to a
regularized classification loss. This approach is distinct from existing
kernel-based graph classification models which instead either use feature
engineering or unsupervised learning to define the kernel function.
Experimental results demonstrate that the proposed model outperforms existing
deep learning baseline models on a number of datasets.
