Spanning-Tree Kernels on Graphs

Pattern recognition algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of pattern recognition algorithms becomes available by defining a kernel function on instances of graphs. Graph similarity is the central problem for all learning tasks such as clustering and classification on graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are either computationally expensive or limited in their expressiveness. We try to overcome this problem by defining expressive graph kernels which are based on spanning-tree. Minimum spanning-tree, maximum spanning-tree kernels and mix spanning-tree kernel are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of face images, our spanning-tree kernels show significantly higher classification accuracy than walk-based kernels.