A combined Weisfeiler–Lehman graph kernel for structured data

Abstract

Different graph kernels may correspond to using different notions of similarity or may be using information coming from multiple sources. In this paper, we develop a common method to construct combined graph kernel (CGK) which is based on a family of graph kernels. We define three kinds of CGK. The first one is called the weighted combined graph kernel and is a parametric CGK. The second one is called the accuracy ratio weighted combined graph kernel and is a non-parametric CGK. The third one is called the product combined graph kernel and also belongs to non-parametric CGK. The three kinds of definition of CGK can be applied for constructing CGK based on a family of graph kernels. This family of kernels is demonstrated based on the Weisfeiler–Lehman (WL) sequence of graphs in this paper, including a highly efficient subtree kernel, edge kernel, and shortest path kernel. Experiments demonstrate that our CGK based on WL graph kernels outperforms the corresponding single WL graph kernel on several classification benchmark data sets.