Complex Network Construction of Univariate Chaotic Time Series Based on Maximum Mean Discrepancy

Area of Science:

• Complex Systems Analysis
• Nonlinear Dynamics
• Data Science

Background:

• Analyzing chaotic time series presents significant challenges due to inherent complexity.
• Existing similarity metrics often struggle with the intricacies of chaotic systems.
• A novel approach is needed for robust time series analysis and comparison.

Purpose of the Study:

• To propose a new method for constructing complex networks from univariate chaotic time series.
• To address the challenge of measuring similarity between complex time series.
• To provide a novel tool for the analysis of chaotic dynamics.

Main Methods:

• Transforming univariate time series into a high-dimensional phase space to capture more information.
• Representing time series data using Gaussian mixture models (GMMs).
• Employing maximum mean discrepancy (MMD) to quantify the similarity between GMMs.

Main Results:

• The proposed method successfully transforms time series into a high-dimensional space.
• Gaussian mixture models effectively represent the characteristics of the time series.
• Maximum mean discrepancy provides a reliable measure of similarity between these models.
• Validation using the Lorenz system confirms the method's effectiveness.

Conclusions:

• The developed complex network construction method offers a novel approach to chaotic time series analysis.
• The combination of phase space reconstruction, GMMs, and MMD provides an effective way to measure time series similarity.
• This method enhances the understanding and analysis of complex dynamical systems.