Ground Truth Correspondence Between Nodes to Learn Graph-Matching Edit-Costs
The Graph Edit Distance is the most used distance between Attributed Graphs and it is composed of three main costs on nodes and arcs: Insertion, Deletion and Substitution. We present a method to learn the Insertion and Deletion costs of nodes and edges defined in the Graph Edit Distance, whereas, we define the Edit Cost Substitution data dependent and without parameters (for instance the Euclidean distance). In some applications, the ground truth of the correspondence between some pairs of graphs is available or can be easily deducted. The aim of the method we present is the learning process depends on these few available ground truth correspondences and not to the classification set that in some applications is not available. To learn these costs, the optimisation algorithm tends to minimise the Hamming distance between the ground truth correspondences and the automatically extracted node correspondences. We believe that minimising the Hamming distance makes the matching algorithm to find a good correspondence and so, to increase the recognition ratio of the classification algorithm in a pattern recognition application.
KeywordsGraph edit distance Learning edit costs Hamming distance Continuous optimisation
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- 5.Fan, W.: Graph pattern matching revised for social network analysis. In: ICDT 2012, pp. 8–21Google Scholar
- 6.Qi, X., Wu, Q., Zhang, Y., Fuller, E., Zhang, C.-Q.: A novel model for DNA sequence similarity analysis based on graph theory. Evolutionary Bioinformatics 7, 149–154 (2011)Google Scholar
- 10.Solé, A., Serratosa, F., Sanfeliu, A.: On the Graph Edit Distance cost: Properties and Applications. Intern. Journal Pattern Recognition & Artificial Intelligence 26(5) (2012)Google Scholar
- 16.Moreno, C., Serratosa, F.: Consensus of Two Sets of Correspondences through Optimisation Functions, Pattern Analysis and Applications (2015)Google Scholar
- 17.Mohri, M., Rostamizadeh, A., Talwalkar, A.: Foundations of Machine Learning. The MIT Press (2012). ISBN: 9780262018258Google Scholar
- 23.Serratosa, F.: Speeding up Fast Bipartite Graph Matching trough a new cost matrix. International Journal of Pattern Recognition and Artificial Intelligence 29(2) (2015)Google Scholar
- 29.Delaunay, B.: Sur la sphère vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk 7, 793–800 (1934)Google Scholar
- 30.Nelder, J.A., Mead, R.: Computer Journal 7, 308–313 (1965)Google Scholar