A Graph Kernel from the Depth-Based Representation

Lu Bai, Peng Ren, Xiao Bai, Edwin R. Hancock

Abstract: In this paper we develop a novel graph kernel by matching the depth-based substructures in graphs. We commence by describing how to compute the Shannon entropy of a graph using random walks. We then develop an h-layer depth-based representations for a graph, which is effected by measuring the Shannon entropies of a family of K-layer expansion subgraphs derived from a vertex of the graph. The depth-based representations characterize graphs in terms of high dimensional depth-based complexity information. Based on the new representation, we establish a possible correspondence between vertices of two graphs that allows us to construct a matching-based graph kernel. Experiments on graphs from computer vision datasets demonstrate the effectiveness of our kernel.