The York Research Database

In this paper, we present a hypergraph kernel computed using substructure isomorphism tests. Measuring the isomorphisms between hypergraphs straightforwardly tends to be elusive since a hypergraph may exhibit varying relational orders. We thus transform a hypergraph into a directed line graph. This not only accurately reflects the multiple relationships exhibited by the hypergraph but is also easier to manipulate isomorphism tests. To locate the isomorphisms between hypergraphs through their directed line graphs, we propose a new directed Weisfeiler-Lehman isomorphism test for directed graphs. The new isomorphism test precisely reflects the structure of the directed edges. By identifying the isomorphic substructures of directed graphs, the hypergraph kernel for a pair of hypergraphs is computed by counting the number of pairwise isomorphic substructures from their directed line graphs. We show that our kernel limits tottering that arises in the existing walk and subtree based (hyper)graph kernels. Experiments on challenging (hyper)graph datasets demonstrate the effectiveness of our kernel.