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Classification of random trajectories based on the fractional Lévy stable motion

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  • Janczura, Joanna
  • Burnecki, Krzysztof
  • Muszkieta, Monika
  • Stanislavsky, Aleksander
  • Weron, Aleksander

Abstract

In this paper we propose a new approach for the analysis of experimental data based on the fractional Lévy stable motion (FLSM) and apply it to the Golding–Cox mRNA dataset. The FLSM takes into account non-Gaussian α-stable distributions and is characterized by the memory parameter d=H−1/α, where H is the Hurst exponent. The sign of d indicates the type of diffusion: d=0 for Lévy diffusion, d<0 for subdiffusion and d>0 for superdiffusion. By estimating the memory parameter for trajectories, we obtain their classification along the x and y coordinates independently. It appears that most of the trajectories are subdiffusive, other follow the Lévy-diffusion, but none of them is superdiffusive. We also justify presence of the non-Gaussian α-stable distribution by five different goodness-of-fit tests. We note that the classification procedure presented here can be applied to other experimental data which exhibit a non-Gaussian behavior.

Suggested Citation

  • Janczura, Joanna & Burnecki, Krzysztof & Muszkieta, Monika & Stanislavsky, Aleksander & Weron, Aleksander, 2022. "Classification of random trajectories based on the fractional Lévy stable motion," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009607
    DOI: 10.1016/j.chaos.2021.111606
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    1. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    2. Yann Lanoiselée & Nicolas Moutal & Denis S. Grebenkov, 2018. "Diffusion-limited reactions in dynamic heterogeneous media," Nature Communications, Nature, vol. 9(1), pages 1-16, December.
    3. Agnieszka Wyłomańska & D Robert Iskander & Krzysztof Burnecki, 2020. "Omnibus test for normality based on the Edgeworth expansion," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-36, June.
    4. Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    5. Loch-Olszewska, Hanna, 2019. "Properties and distribution of the dynamical functional for the fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 252-271.
    6. Krzysztof Burnecki & Agnieszka Wylomanska & Aleksei Chechkin, 2015. "Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-23, December.
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