Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A Nested Alignment Graph Kernel Through the Dynamic Time Warping Framework

  • Conference paper
  • First Online:
Graph-Based Representations in Pattern Recognition (GbRPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10310))

Abstract

In this paper, we propose a novel nested alignment graph kernel drawing on depth-based complexity traces and the dynamic time warping framework. Specifically, for a pair of graphs, we commence by computing the depth-based complexity traces rooted at the centroid vertices. The resulting kernel for the graphs is defined by measuring the global alignment kernel, which is developed through the dynamic time warping framework, between the complexity traces. We show that the proposed kernel simultaneously considers the local and global graph characteristics in terms of the complexity traces, but also provides richer statistic measures by incorporating the whole spectrum of alignment costs between these traces. Our experiments demonstrate the effectiveness and efficiency of the proposed kernel.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

References

  1. Alvarez, M.A., Qi, X., Yan, C.: A shortest-path graph kernel for estimating gene product semantic similarity. J. Biomed. Semant. 2, 3 (2011)

    Article  Google Scholar 

  2. Bach, F.R.: Graph kernels between point clouds. In: Proceedings of ICML, pp. 25–32 (2008)

    Google Scholar 

  3. Bai, L., Escolano, F., Hancock, E.R.: Depth-based hypergraph complexity traces from directed line graphs. Pattern Recogn. 54, 229–240 (2016)

    Article  MATH  Google Scholar 

  4. Bai, L., Hancock, E.R.: Graph kernels from the jensen-shannon divergence. J. Math. Imaging Vis. 47(1–2), 60–69 (2013)

    Article  MATH  Google Scholar 

  5. Bai, L., Hancock, E.R.: Depth-based complexity traces of graphs. Pattern Recogn. 47(3), 1172–1186 (2014)

    Article  MATH  Google Scholar 

  6. Bai, L., Hancock, E.R.: Fast depth-based subgraph kernels for unattributed graphs. Pattern Recogn. 50, 233–245 (2016)

    Article  MATH  Google Scholar 

  7. Bai, L., Ren, P., Hancock, E.R.: A hypergraph kernel from isomorphism tests. In: Proceddings of ICPR, pp. 3880–3885 (2014)

    Google Scholar 

  8. Bai, L., Rossi, L., Cui, L., Zhang, Z., Ren, P., Bai, X., Hancock, E.R.: Quantum kernels for unattributed graphs using discrete-time quantum walks. Pattern Recogn. Lett. 87, 96–103 (2017)

    Article  Google Scholar 

  9. Bai, L., Rossi, L., Torsello, A., Hancock, E.R.: A quantum jensen-shannon graph kernel for unattributed graphs. Pattern Recogn. 48(2), 344–355 (2015)

    Article  MATH  Google Scholar 

  10. Bai, L., Rossi, L., Zhang, Z., Hancock, E.R.: An aligned subtree kernel for weighted graphs. In: Proceedings of ICML, pp. 30–39 (2015)

    Google Scholar 

  11. Bai, L., Zhang, Z., Wang, C., Bai, X., Hancock, E.R.: A graph kernel based on the Jensen-Shannon representation alignment. In: Proceedings of IJCAI, pp. 3322–3328 (2015)

    Google Scholar 

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

    Article  Google Scholar 

  13. Conte, D., Ramel, J., Sidere, N., Luqman, M.M., Gaüzère, B., Gibert, J., Brun, L., Vento, M.: A comparison of explicit and implicit graph embedding methods for pattern recognition. In: Proceedings of GbRPR, pp. 81–90 (2013)

    Google Scholar 

  14. Costa, F., De Grave, K.: Fast neighborhood subgraph pairwise distance kernel. In: Proceedings ICML, pp. 255–262 (2010)

    Google Scholar 

  15. Cuturi, M.: Fast global alignment kernels. In: Proceedings of ICML, pp. 929–936 (2011)

    Google Scholar 

  16. Cuturi, M., Vert, J., Birkenes, Ø., Matsui, T.: A kernel for time series based on global alignments. In: Proceedings of ICASSP, pp. 413–416 (2007)

    Google Scholar 

  17. Haasdonk, B., Bahlmann, C.: Learning with distance substitution kernels. In: Rasmussen, C.E., Bülthoff, H.H., Schölkopf, B., Giese, M.A. (eds.) DAGM 2004. LNCS, vol. 3175, pp. 220–227. Springer, Heidelberg (2004). doi:10.1007/978-3-540-28649-3_27

    Chapter  Google Scholar 

  18. Harchaoui, Z., Bach, F.: Image classification with segmentation graph kernels. In: Proceedings of CVPR, pp. 1–8 (2007)

    Google Scholar 

  19. Johansson, F.D., Jethava, V., Dubhashi, D.P., Bhattacharyya, C.: Global graph kernels using geometric embeddings. In: Proceedings of ICML, pp. 694–702 (2014)

    Google Scholar 

  20. Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proceedings of ICML, pp. 321–328 (2003)

    Google Scholar 

  21. Kriege, N., Mutzel, P.: Subgraph matching kernels for attributed graphs. In: Proceedings of ICML (2012)

    Google Scholar 

  22. Kriege, N.M., Giscard, P., Wilson, R.C.: On valid optimal assignment kernels and applications to graph classification. In: Proceedings of NIPS, pp. 1615–1623 (2016)

    Google Scholar 

  23. Ren, P., Aleksić, T., Wilson, R.C., Hancock, E.R.: A polynomial characterization of hypergraphs using the Ihara zeta function. Pattern Recogn. 44(9), 1941–1957 (2011)

    Article  Google Scholar 

  24. Riesen, K., Bunke, H.: Graph classification and clustering based on vector space embedding. World Scientific Publishing Co., Inc., River Edge (2010)

    Book  MATH  Google Scholar 

  25. Rossi, L., Torsello, A., Hancock, E.R.: Measuring graph similarity through continuous-time quantum walks and the quantum jensen-shannon divergence. Phys. Rev. E 91(2), 022815 (2015)

    Article  MathSciNet  Google Scholar 

  26. Rossi, L., Torsello, A., Hancock, E.R., Wilson, R.C.: Characterizing graph symmetries through quantum jensen-shannon divergence. Phys. Rev. E 88(3), 032806 (2013)

    Article  Google Scholar 

  27. Urry, M., Sollich, P.: Random walk kernels and learning curves for gaussian process regression on random graphs. J. Mach. Learn. Res. 14(1), 1801–1835 (2013)

    MathSciNet  MATH  Google Scholar 

  28. Wang, L., Sahbi, H.: Directed acyclic graph kernels for action recognition. In: Proceedings of ICCV, pp. 3168–3175 (2013)

    Google Scholar 

  29. Ye, C., Comin, C.H., Peron, T.K.D., Silva, F.N., Rodrigues, F.A., da Costa, F., Tosello, A., Hancock, E.R.: Thermodynamic characterization of networks using graph polynomials. Phys. Rev. E 92(3), 032810 (2015)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant no. 61503422 and 61602535), the Open Projects Program of National Laboratory of Pattern Recognition, the Young Scholar Development Fund of Central University of Finance and Economics (No. QJJ1540), and the program for innovation research in Central University of Finance and Economics.

Author information

Authors and Affiliations

  1. Central University of Finance and Economics, Beijing, China

    Lu Bai & Lixin Cui

  2. Aston University, Birmingham, UK

    Luca Rossi

  3. University of York, York, UK

    Edwin R. Hancock

Authors
  1. Lu Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luca Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lixin Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Edwin R. Hancock
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Luca Rossi or Lixin Cui .

Editor information

Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Pasquale Foggia

  2. Chinese Academy of Sciences, Beijing, China

    Cheng-Lin Liu

  3. Università degli Studi di Salerno, Fisciano, Italy

    Mario Vento

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Bai, L., Rossi, L., Cui, L., Hancock, E.R. (2017). A Nested Alignment Graph Kernel Through the Dynamic Time Warping Framework. In: Foggia, P., Liu, CL., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2017. Lecture Notes in Computer Science(), vol 10310. Springer, Cham. https://doi.org/10.1007/978-3-319-58961-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-58961-9_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58960-2

  • Online ISBN: 978-3-319-58961-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation