Advertisement

Nonlinear Dynamics

, Volume 75, Issue 4, pp 761–768 | Cite as

Topology identification of complex networks from noisy time series using ROC curve analysis

  • Juan Chen
  • Jun-an Lu
  • Jin Zhou
Original Paper

Abstract

As it is known, there is various unknown information in most real world networks, such as uncertain topological structure and node dynamics. Thus how to identify network topology from dynamical behaviors is an important inverse problem for physics, biology, engineering, and other science disciplines. Recently, with the help of noise, a method to predict network topology has been proposed from the dynamical correlation matrix, which is based on a general, one-to-one correspondence between the correlation matrix and the connection matrix. However, the success rate of this prediction method depends on the threshold, which is related to the coupling strength and noise intensity. Different coupling strength and noise intensity result in different success rate of prediction. To deal with this problem, we select a desirable threshold to improve the success rate of prediction by using Receiver Operating Characteristic (ROC) curve analysis. By the technique of ROC curve analysis, we find that the accuracy and efficiency of topology identification is mainly determined by coupling strengths. The success rate of estimation will be reduced if the coupling is too weak or too strong. The presence of noise facilitates topology identification, but the noise intensity is not always crucial to the effectiveness of topology identification.

Keywords

Complex networks Topology identification Noise ROC curves 

Notes

Acknowledgements

The authors wish to thank Dr. Jie Ren for providing the valuable comments and algorithm. This work is supported by the National Natural Science Foundation of China (Grants No. 11172215, 61004096, 61174028, 61304164, and 61374173).

References

  1. 1.
    Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001) CrossRefGoogle Scholar
  2. 2.
    Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–92 (2002) CrossRefMATHGoogle Scholar
  3. 3.
    Boguñá, M., Pastor-Satorras, R.: Epidemic spreading in correlated complex networks. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 66, 047104 (2002) CrossRefGoogle Scholar
  4. 4.
    Boguñá, M., Pastor-Satorras, R., Vespignani, A.: Absence of epidemic threshold in scale-free networks with degree correlations. Phys. Rev. Lett. 90, 028701 (2003) CrossRefGoogle Scholar
  5. 5.
    Pecora, L.M., Carroll, T.L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109–2112 (1998) CrossRefGoogle Scholar
  6. 6.
    Wang, X.F., Chen, G.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos Appl. Sci. Eng. 12, 187–192 (2002) CrossRefGoogle Scholar
  7. 7.
    Nishikawa, T., Motter, A.E., Lai, Y.-C., Hoppensteadt, F.C.: Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? Phys. Rev. Lett. 91, 014101 (2003) CrossRefGoogle Scholar
  8. 8.
    Yu, D., Righero, M., Kocarev, L.: Estimating topology of network. Phys. Rev. Lett. 97, 188701 (2006) CrossRefGoogle Scholar
  9. 9.
    Wu, Z., Fu, X., Chen, G.: Monitoring the topology of growing dynamical network. Int. J. Mod. Phys. C 21, 1051–1063 (2010) CrossRefMATHGoogle Scholar
  10. 10.
    Zhang, Q., Luo, J., Wan, L.: Parameter identification and synchronization of uncertain general complex networks via adaptive-impulsive control. Nonlinear Dyn. 71, 353–359 (2013) CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Zhou, J., Lu, J.: Topology identification of weighted complex dynamical networks. Physica A 386, 481–491 (2007) CrossRefMathSciNetGoogle Scholar
  12. 12.
    Wu, X.Q.: Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay. Physica A 387, 997–1008 (2008) CrossRefGoogle Scholar
  13. 13.
    Zhou, J., Yu, W.W., Li, X.M., Small, M., Lu, J.A.: Identifying the topology of a coupled FitzHugh–Nagumo neurobiological network via a pinning mechanism. IEEE Trans. Neural Netw. 20, 1679–1684 (2009) CrossRefGoogle Scholar
  14. 14.
    Chen, L., Lu, J.A., Tse, C.K.: Synchronization: an obstacle to identification of network topology. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 56, 310–314 (2009) CrossRefGoogle Scholar
  15. 15.
    Liu, H., Lu, J.A., Lü, J.H., Hill, D.J.: Structure identification of uncertain general complex dynamical networks with time delay. Automatica 45, 1799–1807 (2009) CrossRefMATHGoogle Scholar
  16. 16.
    Zhao, J., Li, Q., Lu, J., Jiang, Z.P.: Topology identification of complex dynamical networks. Chaos 20, 023119 (2010) CrossRefMathSciNetGoogle Scholar
  17. 17.
    Ren, J., Wang, W.-X., Li, B., Lai, Y.-C.: Noise bridges dynamical correlation and topology in complex oscillator networks. Phys. Rev. Lett. 104, 058701 (2010) CrossRefGoogle Scholar
  18. 18.
    Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977) Google Scholar
  19. 19.
    Green, D.M., Swets, J.M.: Signal Detection Theory and Psychophysics. Wiley, New York (1966). ISBN 0-471-32420-5 Google Scholar
  20. 20.
    Metz, C.E.: Basic principles of ROC analysis. Semin. Nucl. Med. 8, 283–298 (1978) CrossRefGoogle Scholar
  21. 21.
    Metz, C.E.: Some practical issues of experimental design and data analysis in radio-logical ROC studies. Invest. Radiol. 24, 234–245 (1989) CrossRefGoogle Scholar
  22. 22.
    Swets, J.A.: Measuring the accuracy of diagnostic systems. Science 240, 1285–1293 (1988) CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Zweig, M.H., Campbell, G.: Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clin. Chem. 39, 561–577 (1993) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of SciencesWuhan University of Science and TechnologyHubeiChina
  2. 2.School of Mathematics and StatisticsWuhan UniversityHubeiChina

Personalised recommendations