Slope Entropy Normalisation by Means of Analytical and Heuristic Reference Values

Area of Science:

• Complexity Science
• Information Theory
• Time Series Analysis

Background:

• Slope Entropy (SlpEn) is a recent entropy calculation method for time series.
• SlpEn uses consecutive value differences and thresholds to create symbolic patterns.
• Standard SlpEn outputs often exceed the [0,1] interval, limiting comparability.

Purpose of the Study:

• To develop a method for normalizing SlpEn values to the [0,1] interval.
• To improve the interpretability and comparability of SlpEn.
• To facilitate the application of SlpEn in time series classification and entropy analysis.

Main Methods:

• A two-step max-min normalization scheme is proposed.
• An initial analytic normalization uses conservative bounds.
• Heuristics on pattern counts in deterministic and random series refine these bounds.

Main Results:

• The proposed method effectively normalizes SlpEn results to the [0,1] interval.
• The normalization enhances the interpretability and comparability of SlpEn.
• A combination of analytic and heuristic normalization proves suitable.

Conclusions:

• The developed normalization method successfully bounds SlpEn within [0,1].
• This normalization improves SlpEn's utility for comparative entropy analysis and time series classification.
• The approach offers a standardized framework for SlpEn application.