Quantifying entropy using recurrence matrix microstates

Area of Science:

• Complex Systems Analysis
• Information Theory
• Time Series Analysis

Background:

• Traditional entropy quantifiers for time series analysis often have limitations.
• Existing methods can be computationally intensive and sensitive to parameters.
• There is a need for robust and efficient entropy measures for diverse time series data.

Purpose of the Study:

• To introduce a new recurrence quantifier for time series analysis based on information entropy.
• To demonstrate the advantages of this novel method over traditional entropy quantifiers.
• To validate the method's performance across different types of systems and data lengths.

Main Methods:

• Defining probabilities based on microstates within a recurrence matrix (small binary submatrices).
• Calculating information entropy using these microstate-defined probabilities.
• Applying the method to both discrete and continuous time series data.

Main Results:

• The new entropy quantifier shows a good correlation with the maximum Lyapunov exponent.
• The method exhibits weak dependence on the vicinity threshold parameter.
• Consistent and accurate results are obtained for both short and long time series segments.
• The approach is computationally efficient, even for large datasets.

Conclusions:

• The proposed recurrence quantifier offers a significant advancement in time series entropy analysis.
• Its robustness, efficiency, and applicability to various systems make it a valuable tool.
• This method provides a precise and computationally feasible alternative for analyzing complex systems.