Bipartite Graph Matching for Computing the Edit Distance of Graphs
In the field of structural pattern recognition graphs constitute a very common and powerful way of representing patterns. In contrast to string representations, graphs allow us to describe relational information in the patterns under consideration. One of the main drawbacks of graph representations is that the computation of standard graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for rather small graphs only. One of the most flexible error-tolerant graph similarity measures is based on graph edit distance. In this paper we propose an approach for the efficient compuation of edit distance based on bipartite graph matching by means of Munkres’ algorithm, sometimes referred to as the Hungarian algorithm. Our proposed algorithm runs in polynomial time, but provides only suboptimal edit distance results. The reason for its suboptimality is that implied edge operations are not considered during the process of finding the optimal node assignment. In experiments on semi-artificial and real data we demonstrate the speedup of our proposed method over a traditional tree search based algorithm for graph edit distance computation. Also we show that classification accuracy remains nearly unaffected.
Unable to display preview. Download preview PDF.
- 11.Neuhaus, M., Bunke, H.: An error-tolerant approximate matching algorithm for attributed planar graphs and its application to fingerprint classification. In: Fred, A., Caelli, T.M., Duin, R., Campilho, A., de Ridder, D. (eds.) Structural, Syntactic, and Statistical Pattern Recognition. LNCS, vol. 3138, pp. 180–189. Springer, Heidelberg (2004)Google Scholar
- 14.Boeres, M.C., Ribeiro, C.C., Bloch, I.: A randomized heuristic for scene recognition by graph matching. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 100–113. Springer, Heidelberg (2004)Google Scholar
- 15.Sorlin, S., Solnon, C.: Reactive tabu search for measuring graph similarity. In: Brun, L., Vento, M. (eds.) GbRPR 2005. LNCS, vol. 3434, pp. 172–182. Springer, Heidelberg (2005)Google Scholar
- 19.Neuhaus, M., Riesen, K., Bunke, H.: Fast suboptimal algorithms for the computation of graph edit distance. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 163–172. Springer, Heidelberg (2005)Google Scholar
- 20.Le Saux, B., Bunke, H.: Feature selection for graph-based image classifiers. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 147–154. Springer, Heidelberg (2005)Google Scholar