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Multifractal spectral features enhance classification of anomalous diffusion.

Henrik Seckler1, Ralf Metzler1,2, Damian G Kelty-Stephen3

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Multifractal spectral features effectively distinguish anomalous diffusion models. Neural networks trained on these features, especially from single spectra, show high accuracy in classifying complex diffusion processes.

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Area of Science:

  • Physics
  • Complex Systems
  • Data Science

Background:

  • Anomalous diffusion processes exhibit nonstandard scaling, challenging their classification.
  • A prior study established a multifractal formalism framework for anomalous diffusion.

Purpose of the Study:

  • To evaluate multifractal spectral features for distinguishing anomalous diffusion trajectories.
  • To assess the performance of neural networks using these features against five standard models.

Main Methods:

  • Generated 10^6 trajectories from five anomalous diffusion models.
  • Extracted multiple multifractal spectra per trajectory.
  • Analyzed neural network performance with varying feature sets and integrated multifractal spectra.

Main Results:

  • Moving-window and p-variation features yielded high classification accuracy.
  • Multifractal spectral features, particularly from three spectra, showed strong discriminatory potential.
  • A neural network trained solely on one multifractal spectrum outperformed other feature groups.

Conclusions:

  • Multifractal spectral features significantly enhance machine learning classification of anomalous diffusion.
  • Single multifractal spectra possess potent discriminatory power for complex diffusion analysis.