Abstract
Graph edit distance (GED) is a widely used dissimilarity measure between graphs. It is a natural metric for comparing graphs and respects the nature of the underlying space, and provides interpretability for operations on graphs. As a key ingredient of the GED, the choice of edit cost functions has a dramatic effect on the GED and therefore the classification or regression performances. In this paper, in the spirit of metric learning, we propose a strategy to optimize edit costs according to a particular prediction task, which avoids the use of predefined costs. An alternate iterative procedure is proposed to preserve the distances in both the underlying spaces, where the update on edit costs obtained by solving a constrained linear problem and a re-computation of the optimal edit paths according to the newly computed costs are performed alternately. Experiments show that regression using the optimized costs yields better performances compared to random or expert costs.
This research was supported by CSC (China Scholarship Council), the French national research agency (ANR) under the grant APi (ANR-18-CE23-0014), the ANR “Investissements d’avenir” program ANR-19-P3IA-0001 (PRAIRIE 3IA Institute) and grant ESIGMA ANR-17-CE23-0010.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note the GED will be null when comparing two isomorphic graphs.
- 2.
Code available at https://gitlab.insa-rouen.fr/bgauzere/fit-distances.
References
Abu-Aisheh, Z., et al.: Graph edit distance contest: results and future challenges. Pattern Recogn. Lett. 100, 96–103 (2017)
Altman, N.S.: An introduction to kernel and nearest-neighbor nonparametric regression. Am. Stat. 46(3), 175–185 (1992)
Balcilar, M., Renton, G., Héroux, P., Gaüzère, B., Adam, S., Honeine, P.: When spectral domain meets spatial domain in graph neural networks. In: Proceedings of ICML 2020 - Workshop on Graph Representation Learning and Beyond (GRL+ 2020), Vienna, Austria, 12–18 July 2020
Bellet, A., Habrard, A., Sebban, M.: Good edit similarity learning by loss minimization. Mach. Learn. 89(1–2), 5–35 (2012)
Bellet, A., Habrard, A., Sebban, M.: A survey on metric learning for feature vectors and structured data. arXiv preprint arXiv:1306.6709 (2013)
Blumenthal, D.B., Boria, N., Gamper, J., Bougleux, S., Brun, L.: Comparing heuristics for graph edit distance computation. VLDB J. 29(1), 419–458 (2020)
Bougleux, S., Brun, L., Carletti, V., Foggia, P., Gaüzère, B., Vento, M.: Graph edit distance as a quadratic assignment problem. Pattern Recogn. Lett. 87, 38–46 (2015)
Bronstein, M.M., Bruna, J., LeCun, Y., Szlam, A., Vandergheynst, P.: Geometric deep learning: going beyond Euclidean data. IEEE Signal Process. Mag. 34(4), 18–42 (2017)
Bunke, H.: Error correcting graph matching: on the influence of the underlying cost function. IEEE Trans. Pattern Anal. Mach. Intell. 21(9), 917–922 (1999). https://doi.org/10.1109/34.790431
Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recogn. Lett. 1(4), 245–253 (1983)
Cherqaoui, D., Villemin, D.: Use of a neural network to determine the boiling point of alkanes. J. Chem. Soc. Faraday Trans. 90, 97–102 (1994)
Cherqaoui, D., Villemin, D., Mesbah, A., Cense, J.M., Kvasnicka, V.: Use of a neural network to determine the normal boiling points of acyclic ethers, peroxides, acetals and their sulfur analogues. J. Chem. Soc. Faraday Trans. 90, 2015–2019 (1994)
Cortés, X., Conte, D., Cardot, H.: Learning edit cost estimation models for graph edit distance. Pattern Recogn. Lett. 125, 256–263 (2019). https://doi.org/10.1016/j.patrec.2019.05.001
Cortés, X., Serratosa, F.: Learning graph-matching edit-costs based on the optimality of the oracle’s node correspondences. Pattern Recogn. Lett. 56, 22–29 (2015)
Cristianini, N., Shawe-Taylor, J., Elisseeff, A., Kandola, J.: On kernel-target alignment. In: Advances in Neural Information Processing Systems, pp. 367–373 (2002)
Diamond, S., Boyd, S.: CVXPY: a python-embedded modeling language for convex optimization. J. Mach. Learn. Res. 17(1), 2909–2913 (2016)
Gibert, J., Valveny, E., Bunke, H.: Graph embedding in vector spaces by node attribute statistics. Pattern Recogn. 45(9), 3072–3083 (2012)
Honeine, P., Richard, C.: Preimage problem in kernel-based machine learning. IEEE Signal Process. Mag. 28(2), 77–88 (2011)
Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. SIAM, Philadelphia (1995)
Neuhaus, M., Bunke, H.: A probabilistic approach to learning costs for graph edit distance. Proc. ICPR 3(C), 389–393 (2004)
Neuhaus, M., Bunke, H.: Self-organizing maps for learning the edit costs in graph matching. IEEE Trans. Syst. Man Cybern. 35(3), 503–514 (2005)
Neuhaus, M., Bunke, H.: Automatic learning of cost functions for graph edit distance. Inf. Sci. 177(1), 239–247 (2007). https://doi.org/10.1016/j.ins.2006.02.013
Ontañón, S.: An overview of distance and similarity functions for structured data. Artif. Intell. Rev. (2020). https://doi.org/10.1007/s10462-020-09821-w
Riesen, K.: Structural Pattern Recognition with Graph Edit Distance. ACVPR. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27252-8
Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo, N., et al. (eds.) SSPR /SPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89689-0_33
Ristad, E.S., N.yianilos, P.: Learning string-edit distance. IEEE Trans. Pattern Anal. Mach. Intell. 20(5), 522–532 (1998). https://doi.org/10.1109/34.682181
Sanfeliu, A., Fu, K.S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Trans. Systems, Man Cybern. 13(3), 353–362 (1983)
Shervashidze, N., Schweitzer, P., Van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-lehman graph kernels. J. Mach. Learn. Res. 12(9) (2011)
Virtanen, P., et al.: Scipy 1.0: fundamental algorithms for scientific computing in python. Nat. Method 17(3), 261–272 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Jia, L., Gaüzère, B., Yger, F., Honeine, P. (2021). A Metric Learning Approach to Graph Edit Costs for Regression. In: Torsello, A., Rossi, L., Pelillo, M., Biggio, B., Robles-Kelly, A. (eds) Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2021. Lecture Notes in Computer Science(), vol 12644. Springer, Cham. https://doi.org/10.1007/978-3-030-73973-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-030-73973-7_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-73972-0
Online ISBN: 978-3-030-73973-7
eBook Packages: Computer ScienceComputer Science (R0)
