A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks

Area of Science:

• Nonlinear dynamics
• Information theory
• Machine learning

Background:

• Entropy estimation is crucial for analyzing time series complexity in nonlinear systems.
• Existing entropy methods suffer from parameter sensitivity, limiting their reliability.
• A need exists for robust and accurate time series entropy measures.

Purpose of the Study:

• To propose a new method for time series entropy estimation using a LogNNet neural network.
• To introduce NNetEn as an entropy measure based on image classification accuracy.
• To develop a new time series characteristic, 'time series learning inertia'.

Main Methods:

• Utilizing the LogNNet neural network model for entropy estimation.
• Filling the LogNNet reservoir matrix with time series elements via a specific algorithm.
• Employing MNIST-10 image classification accuracy as the entropy measure (NNetEn).
• Introducing and utilizing 'time series learning inertia' to characterize learning rates.

Main Results:

• NNetEn demonstrated a direct correlation between time series complexity and classification accuracy.
• The method proved robust and efficient across various time series types (chaotic, periodic, random, binary, constant).
• NNetEn showed superior robustness and accuracy compared to traditional entropy estimation techniques.

Conclusions:

• NNetEn offers a novel, parameter-independent approach to time series entropy estimation.
• The method accurately quantifies time series complexity and predictability.
• NNetEn is a promising tool for practical applications in nonlinear system analysis and control.