Clustering of time-evolving scaling dynamics in a complex signal

Area of Science:

• Physics
• Physiology
• Complex Systems Analysis

Background:

• Complex time series are prevalent in physics and physiology.
• Traditional multifractal analysis tools like the multifractal spectrum overlook the temporal evolution of scaling dynamics.

Purpose of the Study:

• To introduce scaling maps for analyzing the time evolution of scaling dynamics in complex time series.
• To develop a methodology for automatic clustering of scaling regimes within signals.
• To enable real-time detection of changing dynamics in complex systems.

Main Methods:

• Development of scaling maps to incorporate the time dimension into multifractal analysis.
• Methodology for automatic clustering of identified scaling regimes.
• Application to time-evolving correlated and uncorrelated noise signals.
• Demonstration on cardiac interbeat interval data from healthy and pathological states.

Main Results:

• Scaling maps successfully capture the temporal evolution of scaling dynamics.
• The clustering methodology effectively identifies and groups distinct scaling regimes.
• The approach is validated on both synthetic and real-world physiological data.

Conclusions:

• Scaling maps offer a significant advancement over traditional multifractal analysis by including temporal dynamics.
• The developed methodology provides a robust tool for analyzing and classifying dynamic regimes in complex time series.
• This approach has potential applications in real-time monitoring and understanding of dynamic processes.