Continuous ordinal patterns: Creating a bridge between ordinal analysis and deep learning.

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Data Science

Background:

• Ordinal patterns offer a computationally efficient method for time series analysis.
• Traditional ordinal analysis lacks the ability to incorporate local amplitude information.
• Bridging ordinal analysis with deep learning can enhance performance on complex tasks.

Purpose of the Study:

• To generalize the ordinal pattern approach by defining patterns in a continuous manner.
• To integrate local amplitude information into ordinal pattern analysis.
• To achieve performance comparable to deep learning methods while maintaining simplicity and interpretability.

Main Methods:

• Generalization of ordinal patterns to a continuous domain.
• Optimization of continuous ordinal patterns for specific analytical problems.
• Application to synthetic time series, brain activity data, and air transport dynamics.

Main Results:

• The generalized ordinal pattern approach effectively incorporates local amplitude.
• Performance comparable to deep learning achieved on real-world classification problems.
• Demonstrated utility in analyzing synthetic, biological, and logistical time series data.

Conclusions:

• Continuous ordinal patterns offer a powerful and versatile tool for time series analysis.
• This novel approach combines the strengths of traditional ordinal methods and deep learning.
• The method shows potential for assessing various dynamical aspects, including time irreversibility.