Abstract
Computing a graph prototype may constitute a core element for clustering or classification tasks. However, its computation is an NP-Hard problem, even for simple classes of graphs. In this paper, we propose an efficient approach based on block coordinate descent to compute a generalized median graph from a set of graphs. This approach relies on a clear definition of the optimization process and handles labeling on both edges and nodes. This iterative process optimizes the edit operations to perform on a graph alternatively on nodes and edges. Several experiments on different datasets show the efficiency of our approach.
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
Similar content being viewed by others
Notes
- 1.
GREYC Chemistry dataset: https://brunl01.users.greyc.fr/CHEMISTRY/.
References
Bougleux, S., Gaüzère, B., Brun, L.: Graph edit distance as a quadratic program. In: International Conference on Pattern Recognition, pp. 1701–1706 (2016). https://doi.org/10.1109/ICPR.2016.7899881
Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recogn. Lett. 1(4), 245–253 (1983). https://doi.org/10.1016/0167-8655(83)90033-8
Chaieb, R., Kalti, K., Luqman, M.M., Coustaty, M., Ogier, J.M., Amara, N.E.B.: Fuzzy generalized median graphs computation: application to content-based document retrieval. Pattern Recogn. 72, 266–284 (2017). https://doi.org/10.1016/j.patcog.2017.07.030
Daller, É., Bougleux, S., Gaüzère, B., Brun, L.: Approximate graph edit distance by several local searches in parallel. In: International Conference on Pattern Recognition Applications and Methods, pp. 149–158 (2018). https://doi.org/10.5220/0006599901490158
Ferrer, M.: Theory and algorithms on the median graph. Application to graph-based classification and clustering. Ph.D. thesis, Universitat Autònoma de Barcelona (2008). http://hdl.handle.net/10803/5788
Ferrer, M., Bardají, I., Valveny, E., Karatzas, D., Bunke, H.: Median graph computation by means of graph embedding into vector spaces. In: Fu, Y., Ma, Y. (eds.) Graph Embedding for Pattern Analysis, pp. 45–71. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-4457-2_3
Ferrer, M., Karatzas, D., Valveny, E., Bardaji, I., Bunke, H.: A generic framework for median graph computation based on a recursive embedding approach. Comput. Vis. Image Underst. 115(7), 919–928 (2011). https://doi.org/10.1016/j.cviu.2010.12.010
Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: Generalized median graph computation by means of graph embedding in vector spaces. Pattern Recogn. 43(4), 1642–1655 (2010). https://doi.org/10.1016/j.patcog.2009.10.013
Hlaoui, A., Wang, S.: Median graph computation for graph clustering. Soft Comput. 10(1), 47–53 (2006). https://doi.org/10.1007/s00500-005-0464-1
Jiang, X., Munger, A., Bunke, H.: On median graphs: properties, algorithms, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 23(10), 1144–1151 (2001). https://doi.org/10.1109/34.954604
Moreno-García, C.F., Serratosa, F., Jiang, X.: Correspondence edit distance to obtain a set of weighted means of graph correspondences. Pattern Recogn. Lett. (2018). https://doi.org/10.1016/j.patrec.2018.08.027
Mukherjee, L., Singh, V., Peng, J., Xu, J., Zeitz, M.J., Berezney, R.: Generalized median graphs and applications. J. Comb. Optim. 17(1), 21–44 (2009). https://doi.org/10.1007/s10878-008-9184-7
Musmanno, L.M., Ribeiro, C.C.: Heuristics for the generalized median graph problem. Eur. J. Oper. Res. 254(2), 371–384 (2016). https://doi.org/10.1016/j.ejor.2016.03.048
Nienkötter, A., Jiang, X.: Improved prototype embedding based generalized median computation by means of refined reconstruction methods. In: Robles-Kelly, A., Loog, M., Biggio, B., Escolano, F., Wilson, R. (eds.) S+SSPR 2016. LNCS, vol. 10029, pp. 107–117. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49055-7_10
Rebagliati, N., Solé-Ribalta, A., Pelillo, M., Serratosa, F.: On the relation between the common labelling and the median graph. In: Gimel’farb, G., et al. (eds.) SSPR /SPR 2012. LNCS, vol. 7626, pp. 107–115. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34166-3_12
Riesen, K.: Structural Pattern Recognition with Graph Edit Distance. ACVPR. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27252-8
Acknowledgments
This work is supported by Région Normandie through RIN AGAC project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Boria, N., Bougleux, S., Gaüzère, B., Brun, L. (2019). Generalized Median Graph via Iterative Alternate Minimizations. In: Conte, D., Ramel, JY., Foggia, P. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2019. Lecture Notes in Computer Science(), vol 11510. Springer, Cham. https://doi.org/10.1007/978-3-030-20081-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-20081-7_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20080-0
Online ISBN: 978-3-030-20081-7
eBook Packages: Computer ScienceComputer Science (R0)
