Bridging time series dynamics and complex network theory with application to electrocardiogram analysis

IEEE Circuits and Systems Magazine

Volumn 12, Issue 4, 2012, Pages 33-46

  Li, Xiang ^a   Yang, Dong ^a   Liu, Xin ^a   Wu, Xiao Mei ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL NEURAL NETWORKS; COLLECTIVE BEHAVIOR; COMPLEX CONNECTIONS; COMPLEX NETWORK THEORY; COMPLEX NETWORKS; CONNECTIVITY PATTERN; ELECTROCARDIOGRAM ANALYSIS; FINANCIAL NETWORKS; HUMAN SOCIETY; INTERACTION NETWORKS; NETWORK SCIENCE; NETWORKED SYSTEMS; SCALE FREE NETWORKS; SMALL WORLDS; TIME SERIES DYNAMICS; TOPOLOGICAL FEATURES; WIRELESS COMMUNICATION NETWORK;

NEURAL NETWORKS; PROTEINS; WIRELESS TELECOMMUNICATION SYSTEMS; WORLD WIDE WEB;

BEHAVIORAL RESEARCH;

EID: 84870530318     PISSN: 1531636X     EISSN: None     Source Type: Journal    
DOI: 10.1109/MCAS.2012.2221521     Document Type: Article

References (66)

1. D. J. Watts and S. H. Strogatz, "Collective dynamics of 'small world' networks, " Nature, vol. 393, pp. 440-442, 1998.
2. A. L. Barabási and R. Albert, "Emergence of scaling in random networks, " Science, vol. 286, pp. 509-512, 1999.
3. S. H. Strogatz, "Exploring complex networks, " Nature, vol. 410, pp. 268-276, 2001. (Pubitemid 32216604)
4. R. Albert and A. L. Barabási, "Statistical mechanics of complex networks, " Rev. Mod. Phys., vol. 74, pp. 47-97, 2002.
5. M. E. J. Newman, "The structure and function of complex networks, " SIAM Rev., vol. 45, pp. 167-256, 2003.
6. X. F. Wang and G. R. Chen, "Complex networks: Small world, scale free and beyond, " IEEE Circuits Syst. Mag., vol. 3, no. 1, pp. 6-21, 2003.
7. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, "Complex networks: Structure and dynamics, " Phys. Rep., vol. 424, pp. 175-308, 2006. (Pubitemid 43135890)
8. L. Cui, S. Kumara, and R. Albert, "Complex networks: An engineering view, " IEEE Circuits Syst. Mag., vol. 10, no. 3, pp. 10-25, 2010.
9. F. C. M. Lau and C. K. Tse, "Application of complex networks to coding, " IEEE Circuits Syst. Mag., vol. 10, no. 3, pp. 38-47, 2010.
10. A. Vespignani, "Modelling dynamical processes in complex socialtechnical systems, " Nature Phys., vol. 8, pp. 32-39, 2012.
11. M. Barahona and L. M. Pecora, "Synchronization in small-world systems, " Phys. Rev. Lett., vol. 89, no. 5, p. 054101, 2002.
12. X. F. Wang and G. Chen, "Synchronization in scale-free dynamical networks: Robustness and fragility, " IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 1, pp. 54-62, 2002. (Pubitemid 34231903)
13. X. Li and G. Chen, "Synchronization and desynchronization of complex dynamical networks: An engineering viewpoint, " IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 11, pp. 1381-1390, 2003.
14. A. Arenas, A. Dias-Guilera, J. Kurths, Y. Moreno, and C. S. Zhou, "Synchronization in complex networks, " Phys. Rep., vol. 469, pp. 93-153, 2008.
15. G. Chen, X. F. Wang, X. Li, and J. Lü, "Some recent advances in complex networks synchronization, " in Recent Advances in Nonlinear Dynamics and Synchronization, K. Kyamakya, Ed. New York: Springer-Verlag, 2009, pp. 3-16.
16. P. DeLellis, M. di Bernardo, T. E. Gorochowski, and G. Russo, "Synchronization and control of complex networks via contraction, adaptation and evolution, " IEEE Circuits Syst. Mag., vol. 10, no. 3, pp. 64-82, 2010.
17. R. Pastor-Satorras and A. Vespingnani, "Epidemic spreading in scale-free networks, " Phys. Rev. Lett., vol. 86, p. 3200, 2001.
18. L. Wang and G. Z. Dai, "Global stability of virus spreading in complex heterogeneous networks, " SIAM J. Appl. Math., vol. 68, no. 5, pp. 1495-1502, 2008.
19. S. Meloni, A. Arenas, and Y. Moreno, "Traffic-driven epidemic spreading in finite-size scale-free networks, " Proc. Nat. Acad. Sci., vol. 106, no. 40, pp. 16897-16902, 2009.
20. C. Castellano and R. Pastor-Satorras, "Thresholds for epidemic spreading in networks, " Phys. Rev. Lett., vol. 105, p. 218701, 2010.
21. R. Parshani, S. Carmi, and S. Havlin, "Epidemic threshold for the susceptible-infectious-susceptible model on random networks, " Phys. Rev. Lett., vol. 104, p. 258701, 2010.
22. L. Wang, X. Li, Y. Q. Zhang, and K. Zhang, "Evolution of scaling emergence in large-scale spatial epidemic spreading, " PLoS ONE, vol. 6, no. 7, p. 21197, 2011.
23. F. C. Santos and J. M. Pacheco, "Scale-free networks provide a unifying framework for the emergence of cooperation, " Phys. Rev. Lett., vol. 95, no. 9, p. 098104, 2005.
24. G. Szabo and G. Fath, "Evolutionary games on graphs, " Phys. Rep., vol. 446, pp. 97-216, 2007.
25. M. A. Nowak and R. Highfield, Super Cooperators: Why We Need Each Other to Succeed. New York: Simon and Schuster, 2011.
26. C. L. Apicella, F. W. Marlowe, J. H. Fowler, and N. A. Christakis, "Social networks and cooperation in hunter-gatherers, " Nature, vol. 481, no. 7382, pp. 497-501, 2012.
27. X. Li, X. F. Wang, and G. Chen, "Pinning a complex dynamical network to its equilibrium, " IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 10, pp. 2074-2087, 2004.
28. X. F. Wang, X. Li, and J. Lu, "Control and flocking of networking systems via pinning, " IEEE Circuits Syst. Mag., vol. 10, no. 3, pp. 83-91, 2010.
29. Y. Liu, J. Slotine, and A. Barabasi, "Controllability of complex networks, " Nature, vol. 473, pp. 167-173, 2011.
30. T. Nepusz and T. Vicsek, "Controlling edge dynamics in complex networks, " Nature Phys., vol. 8, pp. 568-573, 2012.
31. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis. Cambridge, U. K. : Cambridge Univ. Press, 1997.
32. R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. X. Xiang, and J. Kurths, "Recurrence-based time series analysis by means of complex network methods, " Int. J. Bifurcations Chaos, vol. 21, no. 4, pp. 1019-1046, 2011.
33. A. M. Nunez, L. Lacasa, J. P. Gomez, and B. Luque, "Visibility algorithms: A short review, " in New Frontiers in Graph Theory, Y. G. Zhang, Ed. Intech Press, 2012, ch. 6.
34. R. V. Donner and J. F. Donges, "Visibility graph analysis of geophysical time series: Potentials and possible pitfalls, " Acta Geophys., vol. 60, no. 3, pp. 589-623, 2012.
35. J. Zhang and M. Small, "Complex network from pseudoperiodic time series: Topology versus dynamics, " Phys. Rev. Lett., vol. 96, p. 238701, 2006.
36. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuño, "From time series to complex networks: The visibility graph, " Proc. Nat. Acad. Sci., vol. 105, no. 13, pp. 4972-4975, 2008. (Pubitemid 351738493)
37. X. K. Xu, J. Zhang, and M. Small, "Superfamily phenomena and motifs of networks induced from time series, " Proc. Nat. Acad. Sci., vol. 105, no. 50, pp. 19601-19605, 2008.
38. N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, and J. Kurths, "Complex network approach for recurrence analysis of time series, " Phys. Lett. A, vol. 373 no. 46, pp. 4246-4254, 2009.
39. R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, "Recurrence networks: A novel paradigm for nonlinear time series analysis, " New J. Phys., vol. 12, no. 3, p. 033025, 2010.
40. J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, and J. Kurths, "Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution, " Proc. Nat. Acad. Sci., vol. 108, no. 51, pp. 20422-20427, 2011.
41. J. F. Donges, R. V. Donner, K. Rehfeld, N. Marwan, M. H. Trauth, and J. Kurths, "Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis, " Nonlinear Processes Geophys., vol. 18, pp. 545-562, 2011.
42. L. Telesca and M. Lovallo, "Analysis of seismic sequences by using the method of visibility graph, " Europhys. Lett., vol. 97, p. 50002, 2012.
43. Y. Yang, J. B. Wang, H. Yang, and J. Mang, "Visibility graph approach to exchange rate series, " Physica A, vol. 388, pp. 4431-4437, 2009.
44. M. C. Qian, Z. Q. Jiang, and W. X. Zhou, "Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices, " J. Phys. A, Math. Gen., vol. 43, p. 335002, 2010.
45. X. Liu, C. K. Tse, and M. Small, "Complex network structure of musical compositions: Algorithmic generation of appealing music, " Physica A, vol. 389, no. 1, pp. 126-132, 2010.
46. A. Bashan, R. P. Bartsch, J. W. Kantelhardt, S. Havlin, and P. C. Ivanov, "Network physiology reveals relations between network topology and physiological function, " Nature Commun., vol. 3, p. 702, 2012.
47. J. Zhang, J. F. Sun, X. D. Luo, K. Zhang, T. Nakamura, and M. Small, "Characterizing pseudoperiodic time series through the complex network approach, " Physica D, vol. 237, pp. 2856-2865, 2008.
48. H. Malberg, R. Bauernschmitt, A. Voss, T. Walther, R. Faber, H. Stepan, and N. Wessel, "Analysis of cardiovascular oscillations: A new approach to the early prediction of pre-eclampsia, " Chaos, vol. 17, p. 015113, 2007.
49. N. Marwan, N. Wessel, H. Stepan, and J. Kurths, "Recurrence based complex network analysis of cardiovascular variability data to predict pre-eclampsia, " Proc. Biosignal, pp. 1-4, 2010.
50. Z. Shao, "Network analysis of human heartbeat dynamics, " Appl. Phys. Lett., vol. 96, p. 073703, 2010.
51. Physionet. [Online]. Available: http://www. physionet. org/challenge/chaos/
52. Z. Dong and X. Li, "Comment on 'Network analysis of human heartbeat dynamics, '" Appl. Phys. Lett., vol. 96, p. 266101, 2010.
53. Physionet. [Online]. Available: http://www. physionet. org/physiobank/database/nsrdb/
54. Physionet. [Online]. Available: http://www. physionet. org/physiobank/database/chfdb/
55. X. Li and Z. Dong, "Detection and prediction of the onset of human ventricular fibrillation: An approach based on complex network theory, " Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat., vol. 84, p. 062901, 2011.
56. R. Milo, S. Shen-orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, "Network motifs: Simple building blocks of complex networks, " Science, vol. 298, no. 5594, pp. 824-827, 2002. (Pubitemid 35231534)
57. Z. Dong and X. Li, "The study of network motifs induced from discrete time series, " Acta Phys. Sin., vol. 59, no. 3, pp. 1600-1607, 2010.
58. Physionet. [Online]. Available: http://www. physionet. org/physiobank/database/cudb/
59. X. Sun, Y. Zhao, and X. Xue, "Analyzing satial characters of the ECG signal via complex network method, " in Proc. 4th Int. Conf. Biomed. Eng. Informatics, 2011, pp. 1650-1653.
60. B. Bai, Y. Wang, and C. Yang, "Analyzing atrial electricity activity dynamical structure by recurrence complex network, " in Proc. 4th Int. Congr. Image Signal Processing, 2011, pp. 2716-2719.
61. C. Yang, W. Lu, X. Wu, and Z. Fang, "Design and implementation of a new system for whole-atrial epicardial mapping, " Int. J. Bioelectromagnetism, vol. 9, pp. 22-23, 2007.
62. C. Chang and C. Lin, "Training v-support vector classifiers: Theory and algorithms, " Neural Comput., vol. 13, pp. 2119-2147, 2001. (Pubitemid 33595045)
63. D. Yang and X. Li, "Bridge time series and complex networks with a frequency-degree mapping algorithm, " in Proc. IEEE Int. Symp. Circuits Syst., 2012, pp. 910-913.
64. Physionet. [Online]. Available: http://www. physionet. org/cgi-bin/atm/ATM
65. [Online]. Available: http://homepages. fhv. at/ku/karl/VF/filtering. m
66. R. Kerber, L. Becker, and J. Bourland, "Automatic external defibrillators for public access defibrillation: Recommendations for specifying and reporting arrhythmia analysis algorithm performance, incorporating new waveforms, and enhancing safety, " Circulation, vol. 95, pp. 1677-1682, 1997. (Pubitemid 27142847)