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Wavelet-based multiscale similarity measure for complex networks

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Abstract

In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.

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References

  1. J.F. Donges, Y. Zou, N. Marwan, J. Kurths, Eur. Phys. J. Special Topics 174, 157 (2009)

    ADS  Google Scholar 

  2. A. Gozolchiani, K. Yamasaki, O. Gazit, S. Havlin, EPL (Europhys. Lett.) 83, 28005 (2008)

    ADS  Google Scholar 

  3. M.J. Halverson, S.W. Fleming, Hydrol. Earth Syst. Sci. 19, 3301 (2015)

    ADS  Google Scholar 

  4. A. Rheinwalt, B. Goswami, N. Boers, J. Heitzig, N. Marwan, R. Krishnan, J. Kurths, inMachine Learning and Data Mining Approaches to Climate Science, edited by V. Lakshmanan, E. Gilleland, A. McGovern, M. Tingley (Springer International Publishing, Cham, 2015), pp. 23–33

    Google Scholar 

  5. K. Steinhaeuser, A.R. Ganguly, N.V. Chawla, Clim. Dyn. 39, 889 (2012)

    Google Scholar 

  6. K. Yamasaki, A. Gozolchiani, S. Havlin, Phys. Rev. Lett. 100, 228501 (2008)

    ADS  Google Scholar 

  7. A.A. Tsonis, K. Swanson, S. Kravtsov, Geophys. Res. Lett. 34, L13705 (2007)

    ADS  Google Scholar 

  8. R. Quian Quiroga, T. Kreuz, P. Grassberger, Phys. Rev. E 66, 041904 (2002)

    ADS  MathSciNet  Google Scholar 

  9. N. Malik, B. Bookhagen, N. Marwan, J. Kurths, Clim. Dyn. 39, 971 (2012)

    Google Scholar 

  10. U. Ozturk, D. Wendi, I. Crisologo, A. Riemer, A. Agarwal, K. Vogel, J.A. López-Tarazón, O. Korup, Sci. Total Environ. 626, 941 (2018)

    ADS  Google Scholar 

  11. T. Kreuz, M. Mulansky, N. Bozanic, J. Neurophysiol. 113, 3432 (2015)

    Google Scholar 

  12. A.J. Butte, I.S. Kohane, Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements, inBiocomputing 2000 (World Scientific, 1999), pp. 418–429

  13. J.I. Deza, M. Barreiro, C. Masoller, Chaos 25, 033105 (2015)

    ADS  Google Scholar 

  14. M. Paluš, inAdvances in Nonlinear Geosciences, edited by A.A. Tsonis (Springer International Publishing, Cham, 2018), pp. 427–463

  15. M. Rosvall, C.T. Bergstrom, Proc. Natl. Acad. Sci. 104, 7327 (2007)

    ADS  Google Scholar 

  16. A. Agarwal, N. Marwan, M. Rathinasamy, B. Merz, J. Kurths, Nonlinear Process. Geophys. 24, 599 (2017)

    ADS  Google Scholar 

  17. A. Agarwal, N. Marwan, R. Maheswaran, B. Merz, J. Kurths, J. Hydrol. 563, 802 (2018)

    ADS  Google Scholar 

  18. U. Ozturk, N. Marwan, O. Korup, H. Saito, A. Agarwal, M.J. Grossman, M. Zaiki, J. Kurths, Chaos 28, 075301 (2018)

    ADS  MathSciNet  Google Scholar 

  19. A. Abbasi, L. Hossain, inComplex Networks, edited by R. Menezes, A. Evsukoff, M.C. González (Springer, Berlin, Heidelberg, 2013), pp. 1–7

  20. P. Basaras, D. Katsaros, L. Tassiulas, Computer 46, 24 (2013)

    Google Scholar 

  21. N. Boers, A. Rheinwalt, B. Bookhagen, H.M.J. Barbosa, N. Marwan, J. Marengo, J. Kurths, Geophys. Res. Lett. 41, 7397 (2014)

    ADS  Google Scholar 

  22. N. Boers, R.V. Donner, B. Bookhagen, J. Kurths, Clim. Dyn. 45, 619 (2015)

    Google Scholar 

  23. N. Marwan, J.H. Feldhoff, R.V. Donner, J.F. Donges, J. Kurths, IEICE Proc. Ser. 1, 231 (2014)

    Google Scholar 

  24. K. Li, Z.Gao, X. Zhao, Physica A 387, 2981 (2008)

    ADS  Google Scholar 

  25. D. Looney, A. Hemakom, D.P. Mandic, Proc. R. Soc. A: Math. Phys. Eng. Sci. 471, 20140709 (2014)

    ADS  Google Scholar 

  26. A. Molini, G.G. Katul, A. Porporato, J. Geophys. Res. 115, 14123 (2010)

    Google Scholar 

  27. C.A. Varotsos, M.N. Efstathiou, A.P. Cracknell, Atmospheric Chem. Phys. 13, 5243 (2013)

    ADS  Google Scholar 

  28. J.A. Hatala, M. Detto, D.D. Baldocchi, Geophys. Res. Lett. 39, L06409 (2012)

    ADS  Google Scholar 

  29. C. Sturtevant, B.L. Ruddell, S.H. Knox, J. Verfaillie, J.H. Matthes, P.Y. Oikawa, D. Baldocchi, J. Geophys. Res.: Biogeosci. 121, 188 (2016)

    Google Scholar 

  30. E. Casagrande, B. Mueller, D.G. Miralles, D. Entekhabi, A. Molini, J. Geophys. Res.: Atmos. 120, 7555 (2015)

    ADS  Google Scholar 

  31. D.G. Miralles, A.J. Teuling, C.C. van Heerwaarden, J. Vilà-Guerau de Arellano, Nat. Geosci. 7, 345 (2014)

    ADS  Google Scholar 

  32. G.S. Okin, A.J. Parsons, J. Wainwright, J.E. Herrick, B.T. Bestelmeyer, D.C. Peters, E.L. Fredrickson, BioScience 59, 237 (2009)

    Google Scholar 

  33. D.P.C. Peters, B.T. Bestelmeyer, M.G. Turner, Ecosystems 10, 790 (2007)

    Google Scholar 

  34. J. Fernández-Macho, Physica A 391, 1097 (2012)

    ADS  Google Scholar 

  35. R.M. Lark, R. Webster, Eur. J. Soil Sci. 52, 547 (2001)

    Google Scholar 

  36. C. Yang, B. Olson, J. Si, Neural Comput. 23, 215 (2011)

    Google Scholar 

  37. S. Achard, J. Neurosci. 26, 63 (2006)

    Google Scholar 

  38. P.S. Addison, Physiol. Meas. 26, R155 (2005)

    ADS  Google Scholar 

  39. A. Agarwal, R. Maheswaran, V. Sehgal, R. Khosa, B. Sivakumar, C. Bernhofer, J. Hydrol. 538, 22 (2016)

    ADS  Google Scholar 

  40. H. Eryilmaz, D. Van De Ville, S. Schwartz, P. Vuilleumier, NeuroImage 54, 2481 (2011)

    Google Scholar 

  41. S. Kim, F. In, J. Empir. Financ. 12, 435 (2005)

    Google Scholar 

  42. V.N. Livina, N.R. Edwards, S. Goswami, T.M. Lenton, Q. J. R. Meteor. Soc. 134, 941 (2008)

    ADS  Google Scholar 

  43. S. Podtaev, M. Morozov, P. Frick, Cardiovasc. Eng. 8, 185 (2008)

    Google Scholar 

  44. M. Rathinasamy, R. Khosa, J. Adamowski, S. Ch, G. Partheepan, J. Anand, B. Narsimlu, Water Resour. Res. 50, 9721 (2014)

    ADS  Google Scholar 

  45. J. Richiardi, H. Eryilmaz, S. Schwartz, P. Vuilleumier, D. Van De Ville, NeuroImage 56, 616 (2011)

    Google Scholar 

  46. E. Shusterman, M. Feder, IEEE Trans. Image Process. 3, 207 (1994)

    ADS  Google Scholar 

  47. D.B. Percival, inNonlinear Time Series Analysis in the Geosciences, edited by R.V. Donner, S.M. Barbosa (Springer, Berlin, Heidelberg, 2008), pp. 61–79

  48. A. Agarwal, R. Maheswaran, J. Kurths, R. Khosa, Water Resour. Manag. 30, 4399 (2016)

    Google Scholar 

  49. K. Steinhaeuser, N.V. Chawla, A.R. Ganguly, Stat. Anal. Data Min. 4, 497 (2011)

    MathSciNet  Google Scholar 

  50. W. Hu, B.C. Si, Hydrol. Earth Syst. Sci. 20, 3183 (2016)

    ADS  Google Scholar 

  51. R. Polikar, Fundamental concepts and an overview of the wavelet theory, The Wavelet Tutorial Part I, Rowan University, College of Engineering Web Servers 15, 1996

  52. D.B. Percival, A.T. Walden,Wavelet Methods for Time Series Analysis (Cambridge University Press, Cambridge, 2000)

  53. J.-J. Luo, R. Zhang, S.K. Behera, Y. Masumoto, F.-F. Jin, R. Lukas, T. Yamagata, J. Clim. 23, 726 (2010)

    ADS  Google Scholar 

  54. M.F. Stuecker, A. Timmermann, F.-F. Jin, Y. Chikamoto, W. Zhang, A.T. Wittenberg, E. Widiasih, S. Zhao, Geophys. Res. Lett. 44, 2481 (2017)

    ADS  Google Scholar 

  55. T. Yamagata, S.K. Behera, J.-J. Luo, S. Masson, M.R. Jury, S.A. Rao, inGeophysical Monograph Series, edited by C. Wang, S.P. Xie, J.A. Carton (American Geophysical Union, Washington, D.C., 2013), pp. 189–211

  56. D. Chen, M.A. Cane, A. Kaplan, S.E. Zebiak, D. Huang, Nature 428, 733 (2004)

    ADS  Google Scholar 

  57. M. Newman, M.A. Alexander, T.R. Ault, K.M. Cobb, C. Deser, E. Di Lorenzo, N.J. Mantua, A.J. Miller, S. Minobe, H. Nakamura, N. Schneider, D.J. Vimont, A.S. Phillips, J.D. Scott, C.A. Smith, J. Clim. 29, 4399 (2016)

    ADS  Google Scholar 

  58. M.H. Visbeck, J.W. Hurrell, L. Polvani, H.M. Cullen, Proc. Natl. Acad. Sci. 98, 12876 (2001)

    ADS  Google Scholar 

  59. B. Ferster, B. Subrahmanyam, A. Macdonald, Remote Sens. 10, 331 (2018)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Telegrafenberg, Potsdam, Germany

    Ankit Agarwal, Rathinasamy Maheswaran, Norbert Marwan, Levke Caesar & Jürgen Kurths

  2. Institute of Earth and Environmental Science, University of Potsdam, Potsdam, Germany

    Ankit Agarwal & Jürgen Kurths

  3. GFZ German Research Centre for Geosciences, Section 5.4: Hydrology, Telegrafenberg, Potsdam, Germany

    Ankit Agarwal

  4. Civil Engineering Department, MVGR College of Engineering, Vizianagaram, India

    Rathinasamy Maheswaran

  5. Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany

    Levke Caesar

  6. Institute of Physics, Humboldt Universität zu Berlin, Berlin, Germany

    Jürgen Kurths

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  1. Ankit Agarwal
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  2. Rathinasamy Maheswaran
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  3. Norbert Marwan
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  4. Levke Caesar
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  5. Jürgen Kurths
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Correspondence to Ankit Agarwal.

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Agarwal, A., Maheswaran, R., Marwan, N. et al. Wavelet-based multiscale similarity measure for complex networks. Eur. Phys. J. B 91, 296 (2018). https://doi.org/10.1140/epjb/e2018-90460-6

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  • DOI: https://doi.org/10.1140/epjb/e2018-90460-6

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