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Why Do Big Data and Machine Learning Entail the Fractional Dynamics?

Haoyu Niu1, YangQuan Chen2, Bruce J West3

  • 1Electrical Engineering and Computer Science Department, University of California, Merced, CA 95340, USA.

Entropy (Basel, Switzerland)
|March 6, 2021
PubMed
Summary
This summary is machine-generated.

Fractional calculus (FC) enhances understanding of complex systems, signal processing, and control. This study explores fractional dynamics and stochastic models for big data analytics and machine learning optimization.

Keywords:
big datadiversityfractional calculusfractional dynamicsfractional-order thinkingheavytailednessmachine learningvariability

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Area of Science:

  • Mathematics
  • Complex Systems
  • Machine Learning

Background:

  • Fractional calculus (FC) extends traditional calculus to non-integer orders.
  • Fractional-order thinking (FOT) provides novel approaches to complex systems.
  • FC applications include signal processing, system control, optimization, and creativity.

Purpose of the Study:

  • To explore fractional dynamics and stochastic models.
  • To justify the use of fractional dynamics in big data analytics.
  • To demonstrate the necessity of fractional dynamics in machine learning and optimal randomness.

Main Methods:

  • Discussed fractional dynamics and fractional-order thinking (FOT).
  • Examined rich fractional stochastic models.
  • Presented an optimal randomness case study using a stochastic configuration network (SCN) with heavy-tailed distributions.

Main Results:

  • Fractional dynamics can quantify variability in big data from complex systems.
  • Fractional dynamics offers a more optimal approach to optimization in machine learning.
  • The SCN case study demonstrated the application of optimal randomness with heavy-tailed distributions.

Conclusions:

  • Fractional dynamics and FOT are crucial for advancing big data analytics and machine learning.
  • Future research directions include physics-informed machine learning with fractional dynamics.
  • Fractional models offer enhanced capabilities for complex system analysis and optimization.