Weighted decomposition kernels

We introduce a family of kernels on discrete data structures within the general class of decomposition kernels. A weighted decomposition kernel (WDK) is computed by dividing objects into substructures indexed by a selector. Two substructures are then matched if their selectors satisfy an equality predicate, while the importance of the match is determined by a probability kernel on local distributions fitted on the substructures. Under reasonable assumptions, a WDK can be computed efficiently and can avoid combinatorial explosion of the feature space. We report experimental evidence that the proposed kernel is highly competitive with respect to more complex state-of-the-art methods on a set of problems in bioinformatics.