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A complexity score derived from principal components analysis of nonlinear order measures

Author

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  • Giuliani, Alessandro
  • Colafranceschi, Mauro
  • Webber, Charles L
  • Zbilut, Joseph P

Abstract

The generation of a global “complexity” score for numerical series was derived from a principal components analysis of a group of nonlinear measures of experimental as well simulated series. The concept of complexity was demonstrated to be independent from other descriptors of ordered series such as the amount of variance, the departure from normality and the relative nonstationarity; and to be mainly related to the number of independent elements (or operations) needed to synthesize the series. The possibility of having a univocal ranking of complexity for diverse series opens the way to a wider application of dynamical systems concepts in empirical sciences.

Suggested Citation

  • Giuliani, Alessandro & Colafranceschi, Mauro & Webber, Charles L & Zbilut, Joseph P, 2001. "A complexity score derived from principal components analysis of nonlinear order measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 567-588.
    • Handle: RePEc:eee:phsmap:v:301:y:2001:i:1:p:567-588
    DOI: 10.1016/S0378-4371(01)00427-7
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    Cited by:

    1. Martin, R.R. & Montero, S. & Silva, E. & Bizzarri, M. & Cocho, G. & Mansilla, R. & Nieto-Villar, J.M., 2017. "Phase transitions in tumor growth: V what can be expected from cancer glycolytic oscillations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 762-771.
    2. Dünki, R.M. & Dressel, M., 2006. "Statistics of biophysical signal characteristics and state specificity of the human EEG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 632-650.
    3. Baggio, Rodolfo, 2015. "Looking into the future of complex dynamic systems," MPRA Paper 65549, University Library of Munich, Germany.
    4. Belaire-Franch, Jorge, 2004. "Testing for non-linearity in an artificial financial market: a recurrence quantification approach," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 483-494, August.
    5. Kohestani, Havva & Totonkuban, Mahbubeh & Di Paola, Luisa & Todde, Virginia & Giuliani, Alessandro, 2018. "The basic principles of topology-dynamics relations in networks: An empirical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 584-594.
    6. Alessandro Giuliani & Alessandro Vici, 2024. "On the (Apparently) Paradoxical Role of Noise in the Recognition of Signal Character of Minor Principal Components," Stats, MDPI, vol. 7(1), pages 1-11, January.

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