Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network
We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.
[1] R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics: Correlation and Complexity in Finance. Cambridge, UK: Cambridge University, 2000.
[2] F. Varela, J.-P. Lachaux, E. Rodriguez, and J. Martinerie, "The brainweb:
phase synchronization and large-scale integration", Nat. Rev. Neurosci., vol. 2, pp. 229-239, April 2001.
[3] E. Bullmore and O. Sporns, "Complex brain networks: graph theoretical
analysis of structural and functional system", Nat. Rev. Neurosci., vol. 10,
pp. 186-198, March 2010.
[4] C. W. J. Granger and M. Hatanaka, Spectral analysis of Economic Time
Series. Princeton: Princeton University, 1964.
[5] B. Schelter, M. Winterhalder, R. Dahlhaus, J. Kurths, and J. Timmer,
"Partial phase synchronization for multivariate synchronizing system",
Phys. Rev. Lett., vol. 96, pp. 208103, May 2006.
[6] W. S. Kim, X.-M. Cui, C. N. Yoon, H. X. Ta, and S. K. Han, "Estimating
network link weights from inverse phase synchronization indices", EPL,
vol. 96, pp. 20006, October 2011.
[7] J. Ren, W.-X. Wang, B. Li, and Y.-C. Lai, "Noise bridges dynamical
correlation and topology in coupled networks", Phys. Rev. Lett., vol. 104,
pp. 058701, February 2010.
[8] J. Nawrath, M. C. Romano, M. Thiel, I. Z. Kiss, M. Wickramasinghe, J.
Timmer, J. Kurths, and B. Schelter, "Distinguishing direct from indirect
interactions in oscillatory networks with multiple time scales", Phys. Rev.
Lett., vol. 104, pp. 038701, January 2010.
[9] A.-L. Barabási, R. Albert, and H. Jeong, "Mean-field theory for scale-free
random network", Physica A, 272, (1999) 173.
[10] D. R. Brillinger, Time Series: Data Analysis and Theory. San Francisco:
Holden-Day, Inc., 1981.
[11] R. Dahlhaus, "Graphical interaction models for multivariate time series",
Metrika, vol. 51, pp. 157-172, 2000.
[12] H. X. Ta, C. N. Yoon, L. Holm, and S. K. Han, "Inferring the physical
connectivity of complex networks from their functional dynamics", BMC
Syst. Bio. 4, 70 (2010).
[1] R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics: Correlation and Complexity in Finance. Cambridge, UK: Cambridge University, 2000.
[2] F. Varela, J.-P. Lachaux, E. Rodriguez, and J. Martinerie, "The brainweb:
phase synchronization and large-scale integration", Nat. Rev. Neurosci., vol. 2, pp. 229-239, April 2001.
[3] E. Bullmore and O. Sporns, "Complex brain networks: graph theoretical
analysis of structural and functional system", Nat. Rev. Neurosci., vol. 10,
pp. 186-198, March 2010.
[4] C. W. J. Granger and M. Hatanaka, Spectral analysis of Economic Time
Series. Princeton: Princeton University, 1964.
[5] B. Schelter, M. Winterhalder, R. Dahlhaus, J. Kurths, and J. Timmer,
"Partial phase synchronization for multivariate synchronizing system",
Phys. Rev. Lett., vol. 96, pp. 208103, May 2006.
[6] W. S. Kim, X.-M. Cui, C. N. Yoon, H. X. Ta, and S. K. Han, "Estimating
network link weights from inverse phase synchronization indices", EPL,
vol. 96, pp. 20006, October 2011.
[7] J. Ren, W.-X. Wang, B. Li, and Y.-C. Lai, "Noise bridges dynamical
correlation and topology in coupled networks", Phys. Rev. Lett., vol. 104,
pp. 058701, February 2010.
[8] J. Nawrath, M. C. Romano, M. Thiel, I. Z. Kiss, M. Wickramasinghe, J.
Timmer, J. Kurths, and B. Schelter, "Distinguishing direct from indirect
interactions in oscillatory networks with multiple time scales", Phys. Rev.
Lett., vol. 104, pp. 038701, January 2010.
[9] A.-L. Barabási, R. Albert, and H. Jeong, "Mean-field theory for scale-free
random network", Physica A, 272, (1999) 173.
[10] D. R. Brillinger, Time Series: Data Analysis and Theory. San Francisco:
Holden-Day, Inc., 1981.
[11] R. Dahlhaus, "Graphical interaction models for multivariate time series",
Metrika, vol. 51, pp. 157-172, 2000.
[12] H. X. Ta, C. N. Yoon, L. Holm, and S. K. Han, "Inferring the physical
connectivity of complex networks from their functional dynamics", BMC
Syst. Bio. 4, 70 (2010).
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51951", author = "Won Sup Kim and Xue-Mei Cui and Seung Kee Han", title = "Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network", abstract = "We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.
", keywords = "Chaotic oscillator, complex network, inverse coherence matrix, network estimation.", volume = "6", number = "11", pages = "1452-4", }
