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A Mixed Entropy Local-Global Reproducing Kernel for Attributed Graphs

  • Lixin Cui
  • Lu Bai
  • Luca Rossi
  • Zhihong Zhang
  • Lixiang Xu
  • Edwin R. Hancock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11004)

Abstract

In this paper, we develop a new mixed entropy local-global reproducing kernel for vertex attributed graphs based on depth-based representations that naturally reflect both local and global entropy based graph characteristics. Specifically, for a pair of graphs, we commence by computing the nest depth-based representations rooted at the centroid vertices. The resulting mixed local-global reproducing kernel for a pair of graphs is computed by measuring a basic \(H^1\)-reproducing kernel between their nest representations associated with different entropy measures. We show that the proposed kernel not only reflect both the local and global graph characteristics through the nest depth-based representations, but also reflect rich edge connection information and vertex label information through different kinds of entropy measures. Moreover, since both the required basic \(H^1\)-reproducing kernel and the nest depth-based representation can be computed in a polynomial time, the new proposed kernel processes efficient computational complexity. Experiments on standard graph datasets demonstrate the effectiveness and efficiency of the proposed kernel.

Keywords

Local-global graph kernels Attributed graphs Entropy 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant no. 61602535, 61503422 and 61773415), the Open Projects Program of National Laboratory of Pattern Recognition, and the program for innovation research in Central University of Finance and Economics.

References

  1. 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)CrossRefGoogle Scholar
  2. 2.
    Aronszajn, N.: Theory of reproducing kernels. Trans. Am. Math. Soc. 68(3), 337–404 (1950)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bai, L., Hancock, E.R.: Graph kernels from the Jensen-Shannon divergence. J. Math. Imaging Vis. 47(1–2), 60–69 (2013)CrossRefGoogle Scholar
  4. 4.
    Bai, L., Hancock, E.R.: Depth-based complexity traces of graphs. Pattern Recogn. 47(3), 1172–1186 (2014)CrossRefGoogle Scholar
  5. 5.
    Bai, L., Cui, L., Rossi, L., Xu, L., Hancock, E.R.: A nested alignment graph kernel through the dynamic time warping framework. Pattern Recogn. Lett. (to appear)Google Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2(3), 27 (2011)CrossRefGoogle Scholar
  8. 8.
    Costa, F., De Grave, K.: Fast neighborhood subgraph pairwise distance kernel. In: Proceedings ICML, pp. 255–262 (2010)Google Scholar
  9. 9.
    Dehmer, M., Mowshowitz, A.: A history of graph entropy measures. Inf. Sci. 181(1), 57–78 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Han, L., Escolano, F., Hancock, E.R., Wilson, R.C.: Graph characterizations from von Neumann entropy. Pattern Recogn. Lett. 33(15), 1958–1967 (2012)CrossRefGoogle Scholar
  11. 11.
    Johansson, F., Jethava, V., Dubhashi, D., Bhattacharyya, C.: Global graph kernels using geometric embeddings. In: Proceedings of ICML, pp. 694–702 (2014)Google Scholar
  12. 12.
    Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proceedings of ICML, pp. 321–328 (2003)Google Scholar
  13. 13.
    Kriege, N., Mutzel, P.: Subgraph matching kernels for attributed graphs. In: Proceedings of ICML (2012)Google Scholar
  14. 14.
    Riesen, K., Bunke, H.: Graph Classification and Clustering Based on Vector Space Embedding. World Scientific Publishing Co., Inc., River Edge (2010)Google Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Xu, L., Jiang, X., Bai, L., Xiao, J., Luo, B.: A hybrid reproducing graph kernel based on information entropy. Pattern Recogn. 73, 89–98 (2018)CrossRefGoogle Scholar
  18. 18.
    Xu, L., Niu, X., Xie, J., Abel, A., Luo, B.: A local-global mixed kernel with reproducing property. Neurocomputing 168, 190–199 (2015)CrossRefGoogle Scholar
  19. 19.
    Xu, L., Chen, X., Niu, X., Zhang, C., Luo, B.: A multiple attributes convolution kernel with reproducing property. Pattern Anal. Appl. 20(2), 485–494 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Lixin Cui
    • 1
  • Lu Bai
    • 1
  • Luca Rossi
    • 2
  • Zhihong Zhang
    • 3
  • Lixiang Xu
    • 4
  • Edwin R. Hancock
    • 5
  1. 1.Central University of Finance and EconomicsBeijingChina
  2. 2.Aston UniversityBirminghamUK
  3. 3.Xiamen UniversityXiamenChina
  4. 4.Hefei UniversityHefeiChina
  5. 5.University of YorkYorkUK

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