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Decreasing graph complexity with transitive reduction to improve temporal graph classification

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Abstract

Domains such as bioinformatics, social network analysis, and computer vision, describe relations between entities and cannot be interpreted as vectors or fixed grids. Instead, they are naturally represented by graphs. Often this kind of data evolves over time in a dynamic world, respecting a temporal order being known as temporal graphs. The latter became a challenge since subgraph patterns are very difficult to find and the distance between those patterns may change irregularly over time. While state-of-the-art methods are primarily designed for static graphs and may not capture temporal information, recent works have proposed mapping temporal graphs to static graphs to allow for the use of conventional static kernels approaches. This work presents a new method for temporal graph classification based on transitive reduction, which explores new kernels and Graph Neural Networks for temporal graph classification. We compare the transitive reduction impact on the map to static graphs in terms of accuracy and computational efficiency across different classification tasks. Experimental results demonstrate the effectiveness of the proposed mapping method in improving the accuracy of supervised classification for temporal graphs while maintaining reasonable computational efficiency.

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Data Availability

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References

  1. Amara, A., Hadj Taieb, M.A., Ben Aouicha, M.: Multilingual topic modeling for tracking Covid-19 trends based on facebook data analysis. Appl. Intell. 51(5), 3052–3073 (2021)

    Article  MATH  Google Scholar 

  2. Akhtar, N., Ahamad, M.V.: Graph tools for social network analysis. In: Research Anthology on Digital Transformation, Organizational Change, and the Impact of Remote Work, pp. 485–500. IGI Global, (2021)

  3. Karaivanov, A.: A social network model of covid-19. PLoS ONE 15(10), 0240878 (2020)

    Article  MATH  Google Scholar 

  4. Zhu, Y., Ma, J., Yuan, C., Zhu, X.: Interpretable learning based dynamic graph convolutional networks for Alzheimer’s disease analysis. Inf. Fusion 77, 53–61 (2022)

    Article  MATH  Google Scholar 

  5. Wang, J., Ma, A., Chang, Y., Gong, J., Jiang, Y., Qi, R., Wang, C., Fu, H., Ma, Q., Xu, D.: SCGNN is a novel graph neural network framework for single-cell RNA-SEQ analyses. Nat. Commun. 12(1), 1–11 (2021)

    Article  MATH  Google Scholar 

  6. Zhang, X.-M., Liang, L., Liu, L., Tang, M.-J.: Graph neural networks and their current applications in bioinformatics. Front. Genet. 12, 690049 (2021)

    Article  MATH  Google Scholar 

  7. Pradhyumna, P., Shreya, G., et al.: Graph neural network (gnn) in image and video understanding using deep learning for computer vision applications. In: 2021 Second International Conference on Electronics and Sustainable Communication Systems (ICESC), pp. 1183–1189. IEEE (2021)

  8. Yang, S.: Networks: An Introduction by MEJ Newman: Oxford, UK: Oxford University Press. 720 pp., \$85.00. Taylor & Francis (2013)

  9. Schulz, T.H., Horváth, T., Welke, P., Wrobel, S.: A generalized Weisfeiler-Lehman graph kernel. Mach. Learn. 111(7), 2601–2629 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shervashidze, N., Vishwanathan, S., Petri, T., Mehlhorn, K., Borgwardt, K.: Efficient graphlet kernels for large graph comparison. In: Artificial Intelligence and Statistics, pp. 488–495 (2009). PMLR

  11. Harary, F., Gupta, G.: Dynamic graph models. Math. Comput. Model. 25(7), 79–87 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tadić, B.: Dynamics of directed graphs: the world-wide web. Phys. A 293(1–2), 273–284 (2001)

    Article  MATH  Google Scholar 

  13. Ozcan, S., Astekin, M., Shashidhar, N.K., Zhou, B.: Centrality and scalability analysis on distributed graph of large-scale e-mail dataset for digital forensics. In: 2020 IEEE International Conference on Big Data (Big Data), pp. 2318–2327 (2020). IEEE

  14. Oettershagen, L., Kriege, N.M., Morris, C., Mutzel, P.: Classifying dissemination processes in temporal graphs. Big Data 8(5), 363–378 (2020)

    Article  MATH  Google Scholar 

  15. Meng, X., Li, W., Peng, X., Li, Y., Li, M.: Protein interaction networks: centrality, modularity, dynamics, and applications. Front. Comp. Sci. 15, 1–17 (2021)

    MATH  Google Scholar 

  16. Paulevé, L., Kolčák, J., Chatain, T., Haar, S.: Reconciling qualitative, abstract, and scalable modeling of biological networks. Nat. Commun. 11(1), 4256 (2020)

    Article  MATH  Google Scholar 

  17. Barunik, J., Ellington, M., et al.: Dynamic networks in large financial and economic systems. arXiv preprint arXiv:2007.07842 (2020)

  18. Nonejad, N.: An overview of dynamic model averaging techniques in time-series econometrics. J. Econ. Surv. 35(2), 566–614 (2021)

    Article  MATH  Google Scholar 

  19. Mesbahi, M.: On a dynamic extension of the theory of graphs. In: Proceedings of the 2002 American Control Conference (IEEE Cat. No. CH37301), vol. 2, pp. 1234–1239. IEEE (2002)

  20. Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distrib. Syst. 27(5), 387–408 (2012)

    Article  MATH  Google Scholar 

  21. Wu, H., Cheng, J., Huang, S., Ke, Y., Lu, Y., Xu, Y.: Path problems in temporal graphs. Proc. VLDB Endowment 7(9), 721–732 (2014)

    Article  MATH  Google Scholar 

  22. Michail, O., Spirakis, P.G.: Traveling salesman problems in temporal graphs. Theoret. Comput. Sci. 634, 1–23 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  23. Huang, S., Fu, A.W.-C., Liu, R.: Minimum spanning trees in temporal graphs. In: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, pp. 419–430 (2015)

  24. Jerônimo, C., Patrocínio, Z.K., Malinowski, S., Guimarães, S.J.F., Gravier, G.: A novel method for temporal graph classification based on transitive reduction. In: 2023 IEEE 10th International Conference on Data Science and Advanced Analytics (DSAA), pp. 1–10 (2023). IEEE

  25. Clough, J.R., Gollings, J., Loach, T.V., Evans, T.S.: Transitive reduction of citation networks. J. Complex Netw. 3(2), 189–203 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Dubois, V., Bothorel, C.: Transitive reduction for social network analysis and visualization. In: The 2005 IEEE/WIC/ACM International Conference on Web Intelligence (WI’05), pp. 128–131 (2005). IEEE

  27. Tang, X., Zhou, J., Qiu, Y., Liu, X., Shi, Y., Zhao, J.: One edge at a time: a novel approach towards efficient transitive reduction computation on DAGS. IEEE Access 8, 38010–38022 (2020)

    Article  Google Scholar 

  28. Longa, A., Lachi, V., Santin, G., Bianchini, M., Lepri, B., Lio, P., Scarselli, F., Passerini, A.: Graph neural networks for temporal graphs: State of the art, open challenges, and opportunities. arXiv preprint arXiv:2302.01018 (2023)

  29. Borgwardt, K., Ghisu, E., Llinares-López, F., O’Bray, L., Rieck, B., et al.: Graph kernels: state-of-the-art and future challenges. Found. Trends® Machine Learn. 13(5–6), 531–712 (2020)

    Article  MATH  Google Scholar 

  30. 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: Proceedings of the 33rd International Conference on Neural Information Processing Systems, Article no. 514. Curran Associates Inc., Red Hook, NY

  31. Kumar, S., Zhang, X., Leskovec, J.: Learning dynamic embeddings from temporal interactions. arXiv preprint arXiv:1812.02289 (2018)

  32. Taheri, A., Gimpel, K., Berger-Wolf, T.: Learning to represent the evolution of dynamic graphs with recurrent models. In: Companion Proceedings of the 2019 World Wide Web Conference, pp. 301–307 (2019)

  33. Liljeros, F., Edling, C.R., Amaral, L.A.N.: Sexual networks: implications for the transmission of sexually transmitted infections. Microbes Infect. 5(2), 189–196 (2003)

    Article  MATH  Google Scholar 

  34. Okamoto, K., Chen, W., Li, X.-Y.: Ranking of closeness centrality for large-scale social networks. Lect. Notes Comput. Sci. 5059, 186–195 (2008)

    Article  MATH  Google Scholar 

  35. Khanna, G., Chaturvedi, S.K., Soh, S.: Two-terminal reliability analysis for time-evolving and predictable delay-tolerant networks. Recent Adv. Electr. Electron. Eng. (Formerly Recent Patents on Electrical & Electronic Engineering) 13(2), 236–250 (2020)

    MATH  Google Scholar 

  36. Michail, O.: An introduction to temporal graphs: an algorithmic perspective. Internet Math. 12(4), 239–280 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  37. Wu, B., Yuan, C., Hu, W.: Human action recognition based on context-dependent graph kernels. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2609–2616 (2014)

  38. Kostakos, V.: Temporal graphs. Phys. A 388(6), 1007–1023 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Nikolentzos, G., Siglidis, G., Vazirgiannis, M.: Graph kernels: a survey. J. Artif. Intell. Res. 72, 943–1027 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  40. Srambical, F., Rieck, B.: Filtration surfaces for dynamic graph classification. arXiv preprint arXiv:2309.03616 (2023)

  41. Wang, H., Wu, J., Zhu, X., Chen, Y., Zhang, C.: Time-variant graph classification. IEEE Trans. Actions Syst. Man Cybern. Syst. 50(8), 2883–2896 (2018)

    MATH  Google Scholar 

  42. Oettershagen, L.: Temporal graph algorithms. PhD thesis, Universitäts-und Landesbibliothek Bonn (2022)

  43. Apsemidis, A., Psarakis, S., Moguerza, J.M.: A review of machine learning kernel methods in statistical process monitoring. Comput. Ind. Eng. 142, 106376 (2020)

    Article  MATH  Google Scholar 

  44. Wu, M.C., Lee, S., Cai, T., Li, Y., Boehnke, M., Lin, X.: Rare-variant association testing for sequencing data with the sequence kernel association test. Am. J. Human Genet. 89(1), 82–93 (2011)

    Article  MATH  Google Scholar 

  45. Cao, C., Kwok, D., Edie, S., Li, Q., Ding, B., Kossinna, P., Campbell, S., Wu, J., Greenberg, M., Long, Q.: ktwas: integrating kernel machine with transcriptome-wide association studies improves statistical power and reveals novel genes. Brief. Bioinform. 22(4), 270 (2021)

  46. Cao, C., Kossinna, P., Kwok, D., Li, Q., He, J., Su, L., Guo, X., Zhang, Q., Long, Q.: Disentangling genetic feature selection and aggregation in transcriptome-wide association studies. Genetics 220(2), 216 (2022)

    Article  Google Scholar 

  47. Borgwardt, K.M., Kriegel, H.-P.: Shortest-path kernels on graphs. In: Fifth IEEE International Conference on Data Mining (ICDM’05), p. 8 (2005). IEEE

  48. Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? arXiv preprint arXiv:1810.00826 (2018)

  49. Simonovsky, M., Komodakis, N.: Dynamic edge-conditioned filters in convolutional neural networks on graphs. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3693–3702 (2017)

  50. Morris, C., Kriege, N.M., Bause, F., Kersting, K., Mutzel, P., Neumann, M.: Tudataset: A collection of benchmark datasets for learning with graphs. arXiv preprint arXiv:2007.08663 (2020)

  51. Aho, A.V., Garey, M.R., Ullman, J.D.: The transitive reduction of a directed graph. SIAM J. Comput. 1(2), 131–137 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  52. Chang, C.-C., Lin, C.-J.: Libsvm: a library for support vector machines. ACM Trans. Intell. Syst. Technol. (TIST) 2(3), 1–27 (2011)

    Article  MATH  Google Scholar 

  53. Hagberg, A.A., Schult, D., Swart, P.: NetworkX. Accessed: May 8, 2023 (2008) https://networkx.github.io/

  54. Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., Wang, L., Li, C., Sun, M.: Graph neural networks: a review of methods and applications. AI Open 1, 57–81 (2020)

    Article  MATH  Google Scholar 

  55. Procházka, P., Mareš, M., Dědič, M.: Scalable graph size reduction for efficient GNN application (2022)

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Acknowledgements

The authors thank the Pontifícia Universidade Católica de Minas Gerais – PUC-Minas, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – CAPES – (Grant COFECUB 88887.191730/2018-00, Grant PROAP 88887.842889/2023-00 – PUC/MG and Finance Code 001, STIC-AMSUD 88887.878869/2023-00), STIC-AMSUD 23-STIC-10, the Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq (Grants 407242/2021-0, 306573/2022-9) and Fundação de Apoio à Pesquisa do Estado de Minas Gerais – FAPEMIG (Grant APQ-01079-23), PUC Minas and Inria under the project Learning on graph-based hierarchical methods for image and multimedia data.

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Author notes

  1. Zenilton K. G. Patrocínio Jr., Simon Malinowski, Guillaume Gravier and Silvio Jamil F. Guimarães authors contributed equally to this work.

Authors and Affiliations

  1. ImScience, PUC Minas, R. Dom José Gaspar, 500 - Coração Eucarístico, Belo Horizonte, Minas Gerais, 30535901, Brazil

    Carolina Jerônimo, Zenilton K. G. Patrocínio Jr. & Silvio Jamil F. Guimarães

  2. Univ de Rennes, CNRS, Inria, IRISA, 263 Av. Général Leclerc, 35000, Rennes, France

    Carolina Jerônimo, Simon Malinowski & Guillaume Gravier

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  1. Carolina Jerônimo
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  2. Zenilton K. G. Patrocínio Jr.
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  4. Guillaume Gravier
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  5. Silvio Jamil F. Guimarães
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Contributions

Carolina Jerônimo—she is a PhD candidate and the main author of this paper; Zenilton—he is a collaborator in terms of ideas. He was revised it critically for important intellectual content; Guillaume, Simon, and Silvio—Carolina’s coadvisors. These professors were responsible to several important ideas, in conjunction with Carolina, for the conception and design of the work. Moreover, they are responsible for the PhD funding, and they are coordinators of the project in which this thesis is inside.

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Correspondence to Silvio Jamil F. Guimarães.

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Jerônimo, C., Patrocínio Jr., Z.K.G., Malinowski, S. et al. Decreasing graph complexity with transitive reduction to improve temporal graph classification. Int J Data Sci Anal 19, 229–242 (2025). https://doi.org/10.1007/s41060-024-00632-8

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