Scalable kernels for graphs with continuous attributes

While graphs with continuous node attributes arise in many applications, state-of-the-art graph kernels for comparing continuous-attributed graphs suffer from a high runtime complexity. For instance, the popular shortest path kernel scales as O(n⁴), where n is the number of nodes. In this paper, we present a class of graph kernels with computational complexity O(n²(m + log n + δ² + d)), where δ is the graph diameter, m is the number of edges, and d is the dimension of the node attributes. Due to the sparsity and small diameter of real-world graphs, these kernels typically scale comfortably to large graphs. In our experiments, the presented kernels outperform state-of-the-art kernels in terms of speed and accuracy on classification benchmark datasets.