Including the Magnitude Variability of a Signal in the Ordinal Pattern Analysis

Area of Science:

• Signal processing
• Complexity science
• Machine learning

Background:

• Ordinal Patterns (OPs) are a popular method for signal analysis, transforming signals into symbolic sequences.
• OPs are conceptually clear, simple to implement, robust to noise, and applicable to short signals.
• A major drawback of OPs is the loss of information regarding signal magnitudes during encoding.

Purpose of the Study:

• To propose a method that utilizes signal magnitudes discarded during OP encoding.
• To use these magnitudes as a complementary variable to permutation entropy for improved signal characterization.
• To demonstrate the utility of this approach for feature engineering and enhancing AI classifiers.

Main Methods:

• Developing a technique to recover and utilize signal magnitudes lost in the OP encoding process.
• Combining permutation entropy with the variability of signal magnitudes.
• Applying the enhanced method to synthetic (logistic and Hénon maps) and real-world signals (EEG, power grids).

Main Results:

• The proposed method improves signal characterization when permutation entropy is complemented with signal magnitude variability.
• Results remain explainable, demonstrating the practical applicability of the approach.
• The enhanced features derived from this method can improve the accuracy of AI classifiers.

Conclusions:

• The novel approach effectively overcomes the information loss drawback of traditional OP encoding.
• Complementing permutation entropy with signal magnitude variability offers a more comprehensive signal analysis.
• This method holds significant potential for feature engineering and advancing machine learning applications in signal processing.