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Fractional calculus, using non-integer derivatives, enhances machine learning by providing memory and complex dynamics modeling. This review explores combined techniques for data analysis and optimization, excluding neural networks.

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Area of Science:

  • Applied Mathematics
  • Data Science
  • Machine Learning

Background:

  • Fractional calculus models complex dynamics using non-integer derivatives, capturing spatiotemporal memory.
  • Machine learning excels at pattern recognition and prediction from large datasets.
  • Combining these fields offers novel approaches to data analysis and modeling.

Purpose of the Study:

  • To review and contextualize past combined approaches of fractional calculus and machine learning.
  • To identify and categorize existing techniques for integrating fractional derivatives into machine learning workflows.
  • To motivate machine learning practitioners to adopt fractional calculus tools.

Main Methods:

  • Literature review of combined fractional calculus and machine learning approaches.
  • Categorization of existing methods into preprocessing, machine learning, and optimization.
  • Analysis of fractional derivatives' contributions to machine learning.

Main Results:

  • Fractional derivatives offer powerful preprocessing and feature augmentation.
  • Integration improves physically informed machine learning models.
  • Fractional calculus enhances hyperparameter optimization in machine learning.

Conclusions:

  • Combined fractional calculus and machine learning approaches offer significant potential for data-based problems.
  • Fractional derivatives provide valuable tools for enhancing machine learning techniques.
  • This review highlights opportunities for advancing machine learning through fractional calculus.