A Comparative Study of Three Graph Edit Distance Algorithms

Abstract

Abstract-Graph edit distance (GED) is widely applied to similarity measurement of graphs in inexact graph matching. Due to the difficulty of defining cost functions reasonably, we do research on two GED algorithms without cost function definition: the first is combining edge direction histogram (EDH) and earth mover’s distance (EMD) to estimate the GED; the second is introducing hidden Markov model (HMM) and Kullback-Leibler distance (KLD) into GED algorithm. These algorithms are evaluated theoretically and experimentally, and are compared with the GED from spectral seriation, one of the leading methods for computing GED with cost functions. Theoretical comparison shows that the proposed two cost function free GED algorithms have less complexity and characterize graph structure more effectively than spectral seriation method. Experimental results on image classification demonstrate that time occupied by the EDH-based method is 4.4% that of the spectral seriation method with the same correct classification rate, and correct classification rate of HMM-based method is 3.4% greater than that of the other two methods with 3.3% the time consumed by spectral seriation method. Clustering rate of these three methods is basically the same, but HMM-based and EDH-based methods only consume 3.17% and 5.43% the time of spectral seriation method.