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Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder

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  • Ahmadlou, Mehran
  • Adeli, Hojjat
  • Adeli, Amir

Abstract

Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.

Suggested Citation

  • Ahmadlou, Mehran & Adeli, Hojjat & Adeli, Amir, 2012. "Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4720-4726.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4720-4726
    DOI: 10.1016/j.physa.2012.04.025
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    References listed on IDEAS

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    1. Mocenni, Chiara & Sparacino, Emiliano, 2009. "Identification and simulation of a spatial ecological model in a lake with fractal boundary," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3534-3546.
    2. Liu, Chuang & Zhou, Wei-Xing & Yuan, Wei-Kang, 2010. "Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2675-2681.
    3. Apostolos Serletis & Ioannis Andreadis, 2007. "Random Fractal Structures in North American Energy Markets," World Scientific Book Chapters, in: Quantitative And Empirical Analysis Of Energy Markets, chapter 18, pages 245-255, World Scientific Publishing Co. Pte. Ltd..
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    Citations

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    Cited by:

    1. Mondal, Mitali & Mondal, Arindam & Mondal, Joyati & Patra, Kanchan Kumar & Deb, Argha & Ghosh, Dipak, 2018. "Evidence of centrality dependent fractal behavior in high energy heavy ion interactions: Hint of two different sources," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 230-237.
    2. Peng, Xiaoyi & Zhao, Yi & Small, Michael, 2020. "Identification and prediction of bifurcation tipping points using complex networks based on quasi-isometric mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    3. Lihua Liu & Jing Huang & Huimin Wang, 2020. "Visibility Graph Power Geometric Aggregation Operator and Its Application in Water, Energy and Food Efficiency Evaluation," IJERPH, MDPI, vol. 17(11), pages 1-16, May.
    4. Chen, Shiyu & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2014. "A visibility graph averaging aggregation operator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 1-12.
    5. Lahmiri, Salim, 2018. "Generalized Hurst exponent estimates differentiate EEG signals of healthy and epileptic patients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 378-385.
    6. Bhaduri, Anirban & Bhaduri, Susmita & Ghosh, Dipak, 2017. "Visibility graph analysis of heart rate time series and bio-marker of congestive heart failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 786-795.
    7. Xu, Paiheng & Zhang, Rong & Deng, Yong, 2018. "A novel visibility graph transformation of time series into weighted networks," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 201-208.

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