Kernels for Predictive Graph Mining

In many application areas, graphs are a very natural way of representing structural aspects of a domain. While most classical algorithms for data analysis cannot directly deal with graphs, recently there has been increasing interest in approaches that can learn general classification models from graph-structured data. In this paper, we summarize and review the line of work that we have been following in the last years on making a particular class of methods suitable for predictive graph mining, namely the so-called kernel methods. Firstly, we state a result on fundamental computational limits to the possible expressive power of kernel functions for graphs. Secondly, we present two alternative graph kernels, one based on walks in a graph, the other based on cycle and tree patterns. The paper concludes with empirical evaluation on a large chemical data set.