Abstract
Graph-based machine learning, encompassing Graph Edit Distances (GEDs), Graph Kernels, and Graph Neural Networks (GNNs), offers extensive capabilities and exciting potential. While each model possesses unique strengths for graph challenges, interrelations between their underlying spaces remain under-explored. In this paper, we introduce a novel framework for bridging these distinct spaces via GED cost learning. A supervised metric learning approach serves as an instance of this framework, enabling space alignment through pairwise distances and the optimization of edit costs. Experiments reveal the framework’s potential for enhancing varied tasks, including regression, classification, and graph generation, heralding new possibilities in these fields.
Supported by Swiss National Science Foundation (SNSF) Project No. 200021_188496.
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Notes
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We thank the COBRA lab (Chimie Organique Bioorganique : Réactivité et Analyse) and the ITODYS lab (Le laboratoire Interfaces Traitements Organisation et DYnamique des Systèmes) for providing this dataset.
References
Trinajstic, N.: Chemical Graph Theory. Routledge, New York (2018)
Yi, H.C., You, Z.H., Huang, D.S., Kwoh, C.K.: Graph representation learning in bioinformatics: trends, methods and applications. Brief. Bioinform. 23(1), bbab340 (2022)
Tabassum, S., Pereira, F.S., Fernandes, S., Gama, J.: Social network analysis: an overview. Wiley Interdiscip. Rev. Data Min. Knowl. Discov. 8(5), e1256 (2018)
Jiao, L., et al.: Graph representation learning meets computer vision: a survey. IEEE Trans. Artif. Intell. 4(1), 2–22 (2022)
Goyal, P., Ferrara, E.: Graph embedding techniques, applications, and performance: a survey. Knowl.-Based Syst. 151, 78–94 (2018)
Kriege, N.M., Johansson, F.D., Morris, C.: A survey on graph kernels. Appl. Netw. Sci. 5(1), 1–42 (2020)
Jia, L., Gaüzère, B., Honeine, P.: Graph kernels based on linear patterns: theoretical and experimental comparisons. Expert Syst. Appl. 189, 116095 (2022)
Zhou, J., et al.: Graph neural networks: a review of methods and applications. AI Open 1, 57–81 (2020)
Grattarola, D., Zambon, D., Livi, L., Alippi, C.: Change detection in graph streams by learning graph embeddings on constant-curvature manifolds. IEEE Trans. Neural Netw. Learn. Syst. 31(6), 1856–1869 (2019)
Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recogn. Lett. 1(4), 245–253 (1983)
Fuchs, M., Riesen, K.: A novel way to formalize stable graph cores by using matching-graphs. Pattern Recogn. 131, 108846 (2022)
Neuhaus, Michel, Bunke, Horst: A random walk kernel derived from graph edit distance. In: Yeung, Dit-Yan., Kwok, James T.., Fred, Ana, Roli, Fabio, de Ridder, Dick (eds.) SSPR /SPR 2006. LNCS, vol. 4109, pp. 191–199. Springer, Heidelberg (2006). https://doi.org/10.1007/11815921_20
Neuhaus, M., Bunke, H.: Bridging the Gap Between Graph Edit Distance and Kernel Machines, vol. 68. World Scientific, Singapore (2007)
Gaüzère, B., Brun, L., Villemin, D.: Graph kernels: crossing information from different patterns using graph edit distance. In: Gimel’farb, G., et al. (eds.) SSPR /SPR 2012. LNCS, vol. 7626, pp. 42–50. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34166-3_5
Jia, L., Gaüzère, B., Honeine, P.: A graph pre-image method based on graph edit distances. In: Proceedings of the IAPR Joint International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (S+SSPR), Venice, Italy, 21–22 January 2021
Riba, P., Fischer, A., Lladós, J., Fornés, A.: Learning graph edit distance by graph neural networks. Pattern Recogn. 120, 108132 (2021)
Feng, A., You, C., Wang, S., Tassiulas, L.: KerGNNs: interpretable graph neural networks with graph kernels. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36, pp. 6614–6622 (2022)
Du, S.S., Hou, K., Salakhutdinov, R.R., Poczos, B., Wang, R., Xu, K.: Graph neural tangent kernel: fusing graph neural networks with graph kernels. In: Advances in Neural Information Processing Systems, vol. 32 (2019)
Morris, C., et al.: Weisfeiler and leman go neural: higher-order graph neural networks. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 4602–4609 (2019)
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
Jia, L.: Bridging graph and kernel spaces: a pre-image perspective. Ph.D. thesis, Normandie (2021)
Neuhaus, M., Bunke, H.: A probabilistic approach to learning costs for graph edit distance. Proc. ICPR 3(C), 389–393 (2004)
Bellet, A., Habrard, A., Sebban, M.: Good edit similarity learning by loss minimization. Mach. Learn. 89(1–2), 5–35 (2012)
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
Jia, L., Gaüzère, B., Yger, F., Honeine, P.: A metric learning approach to graph edit costs for regression. In: Torsello, A., Rossi, L., Pelillo, M., Biggio, B., Robles-Kelly, A. (eds.) S+SSPR 2021. LNCS, vol. 12644, pp. 238–247. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-73973-7_23
Garcia-Hernandez, C., Fernández, A., Serratosa, F.: Learning the edit costs of graph edit distance applied to ligand-based virtual screening. Curr. Top. Med. Chem. 20(18), 1582–1592 (2020)
Abu-Aisheh, Z., et al.: Graph edit distance contest: results and future challenges. Pattern Recogn. Lett. 100, 96–103 (2017)
Riesen, K.: Structural Pattern Recognition with Graph Edit Distance. ACVPR, Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27252-8
Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. SIAM, Philadelphia (1995)
Diamond, S., Boyd, S.: CVXPY: a python-embedded modeling language for convex optimization. J. Mach. Learn. Res. 17(1), 2909–2913 (2016)
Virtanen, P., et al.: SciPy 10: fundamental algorithms for scientific computing in python. Nat. Methods 17(3), 261–272 (2020)
Altman, N.S.: An introduction to kernel and nearest-neighbor nonparametric regression. Am. Stat. 46(3), 175–185 (1992)
Boria, N., Bougleux, S., Gaüzère, B., Brun, L.: Generalized median graph via iterative alternate minimizations. In: Conte, D., Ramel, J.-Y., Foggia, P. (eds.) GbRPR 2019. LNCS, vol. 11510, pp. 99–109. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20081-7_10
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Jia, L., Ning, X., Gaüzère, B., Honeine, P., Riesen, K. (2023). Bridging Distinct Spaces in Graph-Based Machine Learning. In: Lu, H., Blumenstein, M., Cho, SB., Liu, CL., Yagi, Y., Kamiya, T. (eds) Pattern Recognition. ACPR 2023. Lecture Notes in Computer Science, vol 14407. Springer, Cham. https://doi.org/10.1007/978-3-031-47637-2_1
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