Beyond randomness: Evaluating measures of information entropy in binary series.

Area of Science:

• Information Theory
• Time Series Analysis
• Biophysics

Background:

• Extracting meaningful information from large datasets is crucial.
• Existing entropy measures (Shannon, permutation, Lempel-Ziv) have limitations in detecting temporal correlations in binary series.
• Binary time series with temporal correlations are common in various fields.

Purpose of the Study:

• To compare information entropy measures in binary series with varying temporal correlations (Hurst exponent H).
• To address the inefficiency of current methods in detecting temporal correlations.
• To propose a novel index, the binary permutation index (BPI), for enhanced pattern discrimination.

Main Methods:

• Numerical and analytical approaches were combined to scrutinize entropy measures.
• The Hurst exponent (H) was used to characterize short- and long-range temporal correlations.
• A new measure, the binary permutation index (BPI), was developed and tested.

Main Results:

• The binary permutation index (BPI) was found to efficiently discriminate patterns in binary series.
• BPI offers advantages over previously used methods in detecting temporal correlations.
• The study demonstrated BPI's application on stock market data, precipitation data, and in vivo electrophysiological recordings.

Conclusions:

• The proposed binary permutation index (BPI) effectively extracts meaningful information from binary time series.
• BPI surpasses existing methods in discriminating randomness and identifying temporal correlations.
• The index has broad applicability across diverse data types, including financial, environmental, and biomedical data.