Learning the Graph Edit Distance by Embedding the Graph Matching

This method is to automatically deduce the insertion, deletion and substitution costs of the Graph edit distance. The method is based on embedding the ground-truth node-to-node mappings into a Euclidean space and learning the edit costs through the hyperplane that splits the nodes into mapped ones and non-mapped ones in this new space. In this way, the algorithm does not need to compute any graph matching process, which is the main drawback of other methods due to its intrin- sic exponential computational complexity. Nevertheless, our learning method has two main restrictions: 1) the insertion and deletion edit costs have to be constants; 2) the substitution edit costs have to be represented as inner products of two vectors. One vector represents certain weights and the other vector represents the distances between attributes. Experimental validation shows that the matching accuracy of this method outperforms the current methods. Furthermore, there is a significant reduction in the runtime in the learning process.This book has main contributions in learning cost based on embedding.