Graph Edit Distance as a Quadratic Program

Calcul de la distance d'édition par minimisation d'une fonctionnelle quadratique

Sébastien Bougleux (1, 2) , Benoit Gaüzère (3, 2, 4) , Luc Brun (1, 2)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 NU - Normandie Université
3 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
4 DocApp - LITIS - Equipe Apprentissage

The graph edit distance (GED) measures the amount of distortion needed to transform a graph into another graph. Such a distance, developed in the context of error-tolerant graph matching, is one of the most flexible tool used in structural pattern recognition. However, the computation of the exact GED is NP-complete. Hence several suboptimal solutions, such as the ones based on bipartite assignments with edition, have been proposed. In this paper we propose a binary quadratic programming problem whose global minimum corresponds to the exact GED. This problem is interpreted as a quadratic assignment problem (QAP) where some constraints on solutions have been relaxed. This allows to adapt the integer projected fixed point algorithm, initially designed for the QAP, to efficiently compute an approximate GED by finding an interesting local minimum. Experiments show that our method remains quite close to the exact GED for datasets composed of small graphs, while keeping low execution times on datasets composed of larger graphs.

Mots clés: Graph edit distance; IPFP

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Sébastien Bougleux, Benoit Gaüzère, Luc Brun. Graph Edit Distance as a Quadratic Program. ICPR 2016 23rd International Conference on Pattern Recognition, Dec 2016, Cancun, Mexico. ⟨hal-01418937⟩