Learning the graph edit distance through embedding the graph matching

• Autores: Shaima Ahmed Algabli
• Directores de la Tesis: Francesc Serratosa Casanelles (dir. tes.)
• Lectura: En la Universitat Rovira i Virgili ( España ) en 2020
• Idioma: español
• Tribunal Calificador de la Tesis: René Alquézar Mancho (presid.), Aïda Valls Mateu (secret.), Benoit Gaüzère (voc.)
• Programa de doctorado: Programa de Doctorado en Ingeniería Informática y Matemáticas de la Seguridad por la Universidad Rovira i Virgili
• Materias:
  • Ciencias tecnológicas
    • Tecnología de las telecomunicaciones
• Enlaces
  • Tesis en acceso abierto en: TDX
• Resumen

  • This thesis presents a learning method 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 thesis has the three main contributions.

    In the first part of the thesis, we have presented a method to learn the edit costs based on embedding the ground truth node-to-node mappings into a Euclidean space. This space has the particularity that the border between substitution and deletions is set as a hyper plane defined by the edit cost parameters.

    The learning method is limited to the applications that substitution costs are represented as a linear combination of a vector of weights and a vector of local costs, weights are normalized to one and insertion and deletion costs are constant. Moreover, the method assumes that the GED is approximated through a sub-optimal algorithm, in which the local information is represented through stars. Note that the weights and costs deduced through our algorithm do not guarantee to be the optimal ones in an optimal graph-matching algorithm neither another sub-optimal graph-matching algorithm based on another local information different from the star.

    Nevertheless, from a practical point of view, our method has three main advantages.

    First, it does not have parameters to be tuned such as a regularization term.

    Second, it is not necessary to impose initial values.

    Third, the Graph edit distance does not need to be computed in the learning process.

    The experimental validation has shown us that the learned parameters are the ones that obtain the highest matching accuracy considering the current methods in the literature. Moreover, our method has a runtime comparable to the fastest method.