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Application of rotational spectrum for correlation dimension estimation

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  • Dlask, Martin
  • Kukal, Jaromir

Abstract

Correlation dimension is one of the many types of fractal dimension. It is usually estimated from a finite number of points from a fractal set using correlation sum and regression in a log-log plot. However, this traditional approach requires a large amount of data and often leads to a biased estimate. The novel approach proposed here can be used for the estimation of the correlation dimension in a frequency domain using the power spectrum of the investigated fractal set. This work presents a new spectral characteristic called “rotational spectrum” and shows its properties in relation to the correlation dimension. The theoretical results can be directly applied to uniformly distributed samples from a given point set. The efficiency of the proposed method was tested on sets with a known correlation dimension using Monte Carlo simulation. The simulation results showed that this method can provide an unbiased estimation for many types of fractal sets.

Suggested Citation

  • Dlask, Martin & Kukal, Jaromir, 2017. "Application of rotational spectrum for correlation dimension estimation," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 256-262.
    • Handle: RePEc:eee:chsofr:v:99:y:2017:i:c:p:256-262
    DOI: 10.1016/j.chaos.2017.04.026
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    References listed on IDEAS

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    1. Yuanhong Liu & Zhiwei Yu & Ming Zeng & Shun Wang, 2015. "Dimension Estimation Using Weighted Correlation Dimension Method," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-10, February.
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    Cited by:

    1. Dlask, Martin & Kukal, Jaromir, 2022. "Hurst exponent estimation of fractional surfaces for mammogram images analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    2. Zhou, Shuang & Wang, Xingyuan & Zhou, Wenjie & Zhang, Chuan, 2022. "Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    3. Dlask, Martin & Kukal, Jaromir, 2018. "Translation and rotation invariant method of Renyi dimension estimation," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 536-541.
    4. Tian, Zhongda, 2020. "Chaotic characteristic analysis of network traffic time series at different time scales," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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    1. Zhou, Shuang & Wang, Xingyuan & Zhou, Wenjie & Zhang, Chuan, 2022. "Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).

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