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

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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.

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References

  1. Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)

    Article  Google Scholar 

  2. Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–92 (2002)

    Article  MATH  Google Scholar 

  3. Boguñá, M., Pastor-Satorras, R.: Epidemic spreading in correlated complex networks. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 66, 047104 (2002)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  5. Pecora, L.M., Carroll, T.L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109–2112 (1998)

    Article  Google Scholar 

  6. Wang, X.F., Chen, G.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos Appl. Sci. Eng. 12, 187–192 (2002)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  8. Yu, D., Righero, M., Kocarev, L.: Estimating topology of network. Phys. Rev. Lett. 97, 188701 (2006)

    Article  Google Scholar 

  9. Wu, Z., Fu, X., Chen, G.: Monitoring the topology of growing dynamical network. Int. J. Mod. Phys. C 21, 1051–1063 (2010)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhou, J., Lu, J.: Topology identification of weighted complex dynamical networks. Physica A 386, 481–491 (2007)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  16. Zhao, J., Li, Q., Lu, J., Jiang, Z.P.: Topology identification of complex dynamical networks. Chaos 20, 023119 (2010)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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. Green, D.M., Swets, J.M.: Signal Detection Theory and Psychophysics. Wiley, New York (1966). ISBN 0-471-32420-5

    Google Scholar 

  20. Metz, C.E.: Basic principles of ROC analysis. Semin. Nucl. Med. 8, 283–298 (1978)

    Article  Google Scholar 

  21. Metz, C.E.: Some practical issues of experimental design and data analysis in radio-logical ROC studies. Invest. Radiol. 24, 234–245 (1989)

    Article  Google Scholar 

  22. Swets, J.A.: Measuring the accuracy of diagnostic systems. Science 240, 1285–1293 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  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 

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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).

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Authors and Affiliations

  1. College of Sciences, Wuhan University of Science and Technology, Hubei, 430081, China

    Juan Chen

  2. School of Mathematics and Statistics, Wuhan University, Hubei, 430072, China

    Jun-an Lu & Jin Zhou

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  1. Juan Chen
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  2. Jun-an Lu
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  3. Jin Zhou
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Correspondence to Jin Zhou.

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Chen, J., Lu, Ja. & Zhou, J. Topology identification of complex networks from noisy time series using ROC curve analysis. Nonlinear Dyn 75, 761–768 (2014). https://doi.org/10.1007/s11071-013-1102-6

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  • DOI: https://doi.org/10.1007/s11071-013-1102-6

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