  In this paper, we show how the Ordered Decomposition DAGs (ODD) kernel
framework, a framework that allows the definition of graph kernels from tree
kernels, allows to easily define new state-of-the-art graph kernels. Here we
consider a fast graph kernel based on the Subtree kernel (ST), and we propose
various enhancements to increase its expressiveness. The proposed DAG kernel
has the same worst-case complexity as the one based on ST, but an improved
expressivity due to an augmented set of features. Moreover, we propose a novel
weighting scheme for the features, which can be applied to other kernels of the
ODD framework. These improvements allow the proposed kernels to improve on the
classification performances of the ST-based kernel for several real-world
datasets, reaching state-of-the-art performances.
