科研之友
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摘要
A number of graph kernel-based methods have been developed with great success in many fields, but very little research has been published that is concerned with a graph kernel in Reproducing Kernel Hilbert Space (RKHS). In this paper, we firstly start with a derived expression for two forms of information entropy of an undirected graph. They are approximated von Neumann entropy and Shannon entropy, and depend on vertex degree statistics. Secondly, we show the basic solution of a generalized differential operator. This solution is a specific reproducing kernel called the H-1-reproducing kernel in H-1-space, and then it is proven to satisfy the condition of Mercer kernel. Thirdly, based on the two aforementioned forms of information entropy and H-1-reproducing kernel, we define two reproducing graph kernels: one is approximated von Neumann entropy reproducing graph kernel (AVNERGK), the other is Shannon entropy reproducing graph kernel (SERGK). And then we prove that they satisfy the condition of Mercer kernel. Finally, to obtain better classification results, we further propose a hybrid reproducing graph kernel (HRGK) based on the two reproducing graph kernels. We use the HRGK as a means to establish the similarity between a pair of graphs. Experimental results reveal that our method gives better classification performance on graphs extracted from several graph datasets.
