Cycle Kernel Based on Spanning Tree

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, shortest path, sub-trees 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 cycle of undirected graph. Cycle kernels of undirected graph is computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of face images, our cycle kernels based on spanning tree of undirected graph show significantly higher classification accuracy than walk kernel.