An Edit Distance Between Graph Correspondences

摘要

The Hamming Distance has been largely used to calculate the dissimilarity of a pair of correspondences (also known as labellings or matchings) between two structures (i.e. sets of points, strings or graphs). Although it has the advantage of being simple in computation, it does not consider the structures that the correspondences relate. In this paper, we propose a new distance between a pair of graph correspondences based on the concept of the edit distance, called Correspondence Edit Distance. This distance takes into consideration not only the mapped elements of the correspondences, but also the attributes on the nodes and edges of the graphs being mapped. In addition to its definition, we also present an efficient procedure for computing the correspondence edit distance in a special case. In the experimental validation, the results delivered using the Correspondence Edit Distance are contrasted against the ones of the Hamming Distance in a case of finding the weighted means between a pair of graph correspondences.