  Graph-structured data arise in many scenarios. A fundamental problem is to
quantify the similarities of graphs for tasks such as classification.
R-convolution graph kernels are positive-semidefinite functions that decompose
graphs into substructures and compare them. One problem in the effective
implementation of this idea is that the substructures are not independent,
which leads to high-dimensional feature space. In addition, graph kernels
cannot capture the high-order complex interactions between vertices. To
mitigate these two problems, we propose a framework called DeepMap to learn
deep representations for graph feature maps. The learned deep representation
for a graph is a dense and low-dimensional vector that captures complex
high-order interactions in a vertex neighborhood. DeepMap extends Convolutional
Neural Networks (CNNs) to arbitrary graphs by generating aligned vertex
sequences and building the receptive field for each vertex. We empirically
validate DeepMap on various graph classification benchmarks and demonstrate
that it achieves state-of-the-art performance.
