Advertisement

Comparing Temporal Graphs Using Dynamic Time Warping

  • Vincent Froese
  • Brijnesh Jain
  • Rolf Niedermeier
  • Malte RenkenEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 882)

Abstract

The links between vertices within many real-world networks change over time. Correspondingly, there has been a recent boom in studying temporal graphs. Proximity-based pattern recognition in temporal graphs requires a (dis)similarity measure to compare different temporal graphs. To this end, we propose to employ dynamic time warping on temporal graphs. We define the dynamic temporal graph warping distance (dtgw) to determine the (dis)similarity of two temporal graphs. Our novel measure is flexible and can be applied in various application domains. We show that computing the dtgw-distance is a challenging (in general NP-hard) optimization problem and we identify some polynomial-time solvable special cases. Moreover, we develop an efficient heuristic which performs well in empirical studies. In experiments on real-word data we show that our dtgw-distance performs favorably in de-anonymizing networks compared to other approaches.

Keywords

Temporal graph alignment Graph matching Vertex signatures NP-hardness Majorize-minimize algorithm 

References

  1. 1.
    Abanda, A., Mori, U., Lozano, J.A.: A review on distance based time series classification. Data Min. Knowl. Disc. 33(2), 378–412 (2019)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Upper Saddle River (1993)zbMATHGoogle Scholar
  3. 3.
    Bagavathi, A., Krishnan, S.: Multi-Net: a scalable multiplex network embedding framework. In: Complex Networks and Their Applications VII. SCI, vol. 813, pp. 119–131. Springer (2019)Google Scholar
  4. 4.
    Braha, D., Bar-Yam, Y.: From centrality to temporary fame: dynamic centrality in complex networks. Complexity 12(2), 59–63 (2006)CrossRefGoogle Scholar
  5. 5.
    Elhesha, R., Sarkar, A., Boucher, C., Kahveci, T.: Identification of co-evolving temporal networks. In: Proceedings of BCB 2018, pp. 591–592. ACM (2018)Google Scholar
  6. 6.
    Fröhlich, H., Wegner, J.K., Sieker, F., Zell, A.: Optimal assignment kernels for attributed molecular graphs. In: Proceedings of ICML 2005, pp. 225–232. ACM (2005)Google Scholar
  7. 7.
    Génois, M., Barrat, A.: Can co-location be used as a proxy for face-to-face contacts? EPJ Data Sci. 7(1), 11 (2018)CrossRefGoogle Scholar
  8. 8.
    Ghosh, S., Das, N., Gonçalves, T., Quaresma, P., Kundu, M.: The journey of graph kernels through two decades. Comput. Sci. Rev. 27, 88–111 (2018)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)CrossRefGoogle Scholar
  10. 10.
    Impagliazzo, R., Paturi, R.: On the complexity of \(k\)-SAT. J. Comput. Syst. Sci. 62(2), 367–375 (2001)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jain, B.J.: On the geometry of graph spaces. Discrete Appl. Math. 214, 126–144 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jouili, S., Tabbone, S.: Graph matching based on node signatures. In: Proceedings of GbRPR 2009. LNCS, vol. 5534, pp. 154–163. Springer (2009)Google Scholar
  13. 13.
    Kostakos, V.: Temporal graphs. Phys. A 388(6), 1007–1023 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Li, A., Cornelius, S.P., Liu, Y.Y., Wang, L., Barabási, A.L.: The fundamental advantages of temporal networks. Science 358(6366), 1042–1046 (2017)CrossRefGoogle Scholar
  15. 15.
    Riesen, K.: Structural pattern recognition with graph edit distance. Springer (2015)Google Scholar
  16. 16.
    Sakoe, H., Chiba, S.: Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans. Acoust. Speech 26(1), 43–49 (1978)CrossRefGoogle Scholar
  17. 17.
    Vijayan, V., Critchlow, D., Milenković, T.: Alignment of dynamic networks. Bioinformatics 33(14), i180–i189 (2017)CrossRefGoogle Scholar
  18. 18.
    Zuo, Y., Liu, G., Lin, H., Guo, J., Hu, X., Wu, J.: Embedding temporal network via neighborhood formation. In: Proceedings of KDD 2018, pp. 2857–2866. ACM (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vincent Froese
    • 1
  • Brijnesh Jain
    • 2
  • Rolf Niedermeier
    • 1
  • Malte Renken
    • 1
    Email author
  1. 1.Faculty IV, Algorithmics and Computational ComplexityTU BerlinBerlinGermany
  2. 2.Faculty IV, Distributed Artificial Intelligence LaboratoryTU BerlinBerlinGermany

Personalised recommendations