Hard c-mean transition network method for analysis of time series

Area of Science:

• Complex Systems Analysis
• Nonlinear Dynamics
• Time Series Analysis

Background:

• Transition networks analyze complex system dynamics but often lack standardized network sizes.
• Existing methods struggle to effectively capture temporal information from diverse time series.

Purpose of the Study:

• To develop a novel method for constructing fixed-size transition networks from time series.
• To enhance the capture of temporal information and nonlinear dynamics in complex systems.

Main Methods:

• Reconstructing phase space using embedding dimension method.
• Clustering state vectors into nodes via hard c-mean algorithm.
• Defining network links based on temporal node succession.

Main Results:

• Successfully distinguished different dynamic behaviors.
• Effectively detected parameter perturbations in dynamical systems.
• Identified seismic airgun signals from acoustic data.

Conclusions:

• The proposed fixed-size transition network method effectively captures nonlinear and nonstationary dynamics.
• The approach demonstrates robustness with short and noisy time series data.