Adaptive matching based kernels for labelled graphs

Abstract

Several kernels over labelled graphs have been proposed in the literatureso far. Most of them are based on the Cross Product (CP) Kernel applied on decompositions of graphs into sub-graphs of specific types. This approach has two main limitations: (i) it is difficult to choose a-priori the appropriate type of sub-graphs for a given problem and (ii) all the sub-graphs of a decomposition participate in the computation of the CP kernel even though many of them might be poorly correlated with the class variable. To tackle these problems we propose a class of graph kernels constructed on the proximity space induced by the graph distances. These graph distances address the aforementioned limitations by learning combinations of different types of graph decompositions and by flexible matching the elements of the decompositions. Experiments performed on a number of graph classification problems demonstrate the effectiveness of the proposed approach. © 2010 Springer-Verlag Berlin Heidelberg.