Approximate graph edit distance computation by means of bipartite graph matching

In recent years, the use of graph based object representation has gained popularity. Simultaneously, graph edit distance emerged as a powerful and flexible graph matching paradigm that can be used to address different tasks in pattern recognition, machine learning, and data mining. The key advantages of graph edit distance are its high degree of flexibility, which makes it applicable to any type of graph, and the fact that one can integrate domain specific knowledge about object similarity by means of specific edit cost functions. Its computational complexity, however, is exponential in the number of nodes of the involved graphs. Consequently, exact graph edit distance is feasible for graphs of rather small size only. In the present paper we introduce a novel algorithm which allows us to approximately, or suboptimally, compute edit distance in a substantially faster way. The proposed algorithm considers only local, rather than global, edge structure during the optimization process. In experiments on different datasets we demonstrate a substantial speed-up of our proposed method over two reference systems. Moreover, it is emprically verified that the accuracy of the suboptimal distance remains sufficiently accurate for various pattern recognition applications.