Approximating Graph Edit Distance Using GNCCP

Abstract

The graph edit distance (GED) is a flexible and widely used dissimilarity measure between graphs. Computing the GED between two graphs can be performed by solving a quadratic assignment problem (QAP). However, the problem is NP complete hence forbidding the computation of the optimal GED on large graphs. To tackle this drawback, recent heuristics are based on a linear approximation of the initial QAP formulation. In this paper, we propose a method providing a better local minimum of the QAP formulation than our previous proposition based on IPFP. We adapt a convex concave regularization scheme initially designed for graph matching which allows to reach better local minimum and avoids the need of an initialization step. Several experiments demonstrate that our method outperforms previous methods in terms of accuracy, with a time still much lower than the computation of a GED.